DOMAIN:
Semiconductor manufacturing process
• CONTEXT:
A complex modern semiconductor manufacturing process is normally under constant surveillance via the monitoring of signals/ variables collected from sensors and or process measurement points. However, not all of these signals are equally valuable in a specific monitoring system. The measured signals contain a combination of useful information, irrelevant information as well as noise. Engineers typically have a much larger number of signals than are actually required. If we consider each type of signal as a feature, then feature selection may be applied to identify the most relevant signals. The Process Engineers may then use these signals to determine key factors contributing to yield excursions downstream in the process. This will enable an increase in process throughput, decreased time to learning and reduce the per unit production costs. These signals can be used as features to predict the yield type. And by analysing and trying out different combinations of features, essential signals that are impacting the yield type can be identified.
• DATA DESCRIPTION:
sensor-data.csv : (1567, 592) The data consists of 1567 examples each with 591 features. The dataset presented in this case represents a selection of such features where each example represents a single production entity with associated measured features and the labels represent a simple pass/fail yield for in house line testing. Target column “ –1” corresponds to a pass and “1” corresponds to a fail and the data time stamp is for that specific test point.
• PROJECT OBJECTIVE:
We will build a classifier to predict the Pass/Fail yield of a particular process entity and analyse whether all the features are required to build the model or not.

In [1]:
#import libraries that will be used for EDA
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
%matplotlib inline
from scipy.stats import zscore
from sklearn.preprocessing import StandardScaler 
from sklearn.model_selection import train_test_split
from sklearn import metrics
from sklearn import preprocessing
from sklearn.metrics import average_precision_score, confusion_matrix, accuracy_score, classification_report, plot_confusion_matrix
import warnings
warnings.filterwarnings('ignore')
from sklearn.decomposition import PCA
pd.set_option('display.max_columns', None)
pd.set_option('display.max_rows', None)
In [2]:
Data = pd.read_csv('signal-data.csv')
In [3]:
Data.shape
# We can see that we have huge number of features
Out[3]:
(1567, 592)
In [4]:
Data.head()
# We can see that datset contains null values, also we have columns with same value
Out[4]:
Time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 Pass/Fail
0 2008-07-19 11:55:00 3030.93 2564.00 2187.7333 1411.1265 1.3602 100.0 97.6133 0.1242 1.5005 0.0162 -0.0034 0.9455 202.4396 0.0 7.9558 414.8710 10.0433 0.9680 192.3963 12.5190 1.4026 -5419.00 2916.50 -4043.75 751.00 0.8955 1.7730 3.0490 64.2333 2.0222 0.1632 3.5191 83.3971 9.5126 50.6170 64.2588 49.3830 66.3141 86.9555 117.5132 61.29 4.515 70.0 352.7173 10.1841 130.3691 723.3092 1.3072 141.2282 1.0 624.3145 218.3174 0.0 4.592 4.841 2834.0 0.9317 0.9484 4.7057 -1.7264 350.9264 10.6231 108.6427 16.1445 21.7264 29.5367 693.7724 0.9226 148.6009 1.0 608.1700 84.0793 NaN NaN 0.0 0.0126 -0.0206 0.0141 -0.0307 -0.0083 -0.0026 -0.0567 -0.0044 7.2163 0.1320 NaN 2.3895 0.9690 1747.6049 0.1841 8671.9301 -0.3274 -0.0055 -0.0001 0.0001 0.0003 -0.2786 0.0 0.3974 -0.0251 0.0002 0.0002 0.1350 -0.0042 0.0003 0.0056 0.0000 -0.2468 0.3196 NaN NaN NaN NaN 0.9460 0.0 748.6115 0.9908 58.4306 0.6002 0.9804 6.3788 15.88 2.639 15.94 15.93 0.8656 3.353 0.4098 3.188 -0.0473 0.7243 0.9960 2.2967 1000.7263 39.2373 123.0 111.3 75.2 46.2000 350.6710 0.3948 0.0 6.78 0.0034 0.0898 0.0850 0.0358 0.0328 12.2566 0.0 4.271 10.284 0.4734 0.0167 11.8901 0.41 0.0506 NaN NaN 1017.0 967.0 1066.0 368.0 0.090 0.048 0.095 2.0 0.9 0.069 0.046 0.7250 0.1139 0.3183 0.5888 0.3184 0.9499 0.3979 0.160 0.0 0.0 20.95 0.333 12.49 16.713 0.0803 5.72 0.0 11.19 65.363 0.0 0.0 0.0 0.0 0.0 0.0 0.292 5.38 20.10 0.296 10.62 10.30 5.38 4.040 16.230 0.2951 8.64 0.0 10.30 97.314 0.0 0.0772 0.0599 0.0700 0.0547 0.0704 0.0520 0.0301 0.1135 3.4789 0.0010 NaN 0.0707 0.0211 175.2173 0.0315 1940.3994 0.0 0.0744 0.0546 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0027 0.0040 0.0 0.0 0.0 0.0 NaN NaN NaN NaN 0.0188 0.0 219.9453 0.0011 2.8374 0.0189 0.0050 0.4269 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0472 40.855 4.5152 30.9815 33.9606 22.9057 15.9525 110.2144 0.1310 0.0 2.5883 0.0010 0.0319 0.0197 0.0120 0.0109 3.9321 0.0 1.5123 3.5811 0.1337 0.0055 3.8447 0.1077 0.0167 NaN NaN 418.1363 398.3185 496.1582 158.3330 0.0373 0.0202 0.0462 0.6083 0.3032 0.0200 0.0174 0.2827 0.0434 0.1342 0.2419 0.1343 0.3670 0.1431 0.0610 0.0 0.0 0.0 6.2698 0.1181 3.8208 5.3737 0.0254 1.6252 0.0 3.2461 18.0118 0.0 0.0 0.0 0.0 0.0 0.0 0.0752 1.5989 6.5893 0.0913 3.0911 8.4654 1.5989 1.2293 5.3406 0.0867 2.8551 0.0 2.9971 31.8843 NaN NaN 0.0 0.0215 0.0274 0.0315 0.0238 0.0206 0.0238 0.0144 0.0491 1.2708 0.0004 NaN 0.0229 0.0065 55.2039 0.0105 560.2658 0.0 0.0170 0.0148 0.0124 0.0114 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0010 0.0013 0.0 0.0 0.0 0.0 NaN NaN NaN NaN 0.0055 0.0 61.5932 0.0003 0.9967 0.0082 0.0017 0.1437 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0151 14.2396 1.4392 5.6188 3.6721 2.9329 2.1118 24.8504 29.0271 0.0 6.9458 2.7380 5.9846 525.0965 0.0000 3.4641 6.0544 0.0 53.6840 2.4788 4.7141 1.7275 6.1800 3.2750 3.6084 18.7673 33.1562 26.3617 49.0013 10.0503 2.7073 3.1158 3.1136 44.5055 42.2737 1.3071 0.8693 1.1975 0.6288 0.9163 0.6448 1.4324 0.4576 0.1362 0.0 0.0 0.0 5.9396 3.2698 9.5805 2.3106 6.1463 4.0502 0.0 1.7924 29.9394 0.0 0.0 0.0 0.0 0.0 0.0 6.2052 311.6377 5.7277 2.7864 9.7752 63.7987 24.7625 13.6778 2.3394 31.9893 5.8142 0.0 1.6936 115.7408 0.0 613.3069 291.4842 494.6996 178.1759 843.1138 0.0000 53.1098 0.0000 48.2091 0.7578 NaN 2.9570 2.1739 10.0261 17.1202 22.3756 0.0 0.0000 0.0000 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 64.6707 0.0000 0.0 0.0 0.0 0.0 NaN NaN NaN NaN 1.9864 0.0 29.3804 0.1094 4.8560 3.1406 0.5064 6.6926 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.0570 4.0825 11.5074 0.1096 0.0078 0.0026 7.116 1.0616 395.570 75.752 0.4234 12.93 0.78 0.1827 5.7349 0.3363 39.8842 3.2687 1.0297 1.0344 0.4385 0.1039 42.3877 NaN NaN NaN NaN NaN NaN NaN NaN 533.8500 2.1113 8.95 0.3157 3.0624 0.1026 1.6765 14.9509 NaN NaN NaN NaN 0.5005 0.0118 0.0035 2.3630 NaN NaN NaN NaN -1
1 2008-07-19 12:32:00 3095.78 2465.14 2230.4222 1463.6606 0.8294 100.0 102.3433 0.1247 1.4966 -0.0005 -0.0148 0.9627 200.5470 0.0 10.1548 414.7347 9.2599 0.9701 191.2872 12.4608 1.3825 -5441.50 2604.25 -3498.75 -1640.25 1.2973 2.0143 7.3900 68.4222 2.2667 0.2102 3.4171 84.9052 9.7997 50.6596 64.2828 49.3404 64.9193 87.5241 118.1188 78.25 2.773 70.0 352.2445 10.0373 133.1727 724.8264 1.2887 145.8445 1.0 631.2618 205.1695 0.0 4.590 4.842 2853.0 0.9324 0.9479 4.6820 0.8073 352.0073 10.3092 113.9800 10.9036 19.1927 27.6301 697.1964 1.1598 154.3709 1.0 620.3582 82.3494 NaN NaN 0.0 -0.0039 -0.0198 0.0004 -0.0440 -0.0358 -0.0120 -0.0377 0.0017 6.8043 0.1358 NaN 2.3754 0.9894 1931.6464 0.1874 8407.0299 0.1455 -0.0015 0.0000 -0.0005 0.0001 0.5854 0.0 -0.9353 -0.0158 -0.0004 -0.0004 -0.0752 -0.0045 0.0002 0.0015 0.0000 0.0772 -0.0903 NaN NaN NaN NaN 0.9425 0.0 731.2517 0.9902 58.6680 0.5958 0.9731 6.5061 15.88 2.541 15.91 15.88 0.8703 2.771 0.4138 3.272 -0.0946 0.8122 0.9985 2.2932 998.1081 37.9213 98.0 80.3 81.0 56.2000 219.7679 0.2301 0.0 5.70 0.0049 0.1356 0.0600 0.0547 0.0204 12.3319 0.0 6.285 13.077 0.5666 0.0144 11.8428 0.35 0.0437 NaN NaN 568.0 59.0 297.0 3277.0 0.112 0.115 0.124 2.2 1.1 0.079 0.561 1.0498 0.1917 0.4115 0.6582 0.4115 1.0181 0.2315 0.325 0.0 0.0 17.99 0.439 10.14 16.358 0.0892 6.92 0.0 9.05 82.986 0.0 0.0 0.0 0.0 0.0 0.0 0.222 3.74 19.59 0.316 11.65 8.02 3.74 3.659 15.078 0.3580 8.96 0.0 8.02 134.250 0.0 0.0566 0.0488 0.1651 0.1578 0.0468 0.0987 0.0734 0.0747 3.9578 0.0050 NaN 0.0761 0.0014 128.4285 0.0238 1988.0000 0.0 0.0203 0.0236 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0064 0.0036 0.0 0.0 0.0 0.0 NaN NaN NaN NaN 0.0154 0.0 193.0287 0.0007 3.8999 0.0187 0.0086 0.5749 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0411 29.743 3.6327 29.0598 28.9862 22.3163 17.4008 83.5542 0.0767 0.0 1.8459 0.0012 0.0440 0.0171 0.0154 0.0069 3.9011 0.0 2.1016 3.9483 0.1662 0.0049 3.7836 0.1000 0.0139 NaN NaN 233.9865 26.5879 139.2082 1529.7622 0.0502 0.0561 0.0591 0.8151 0.3464 0.0291 0.1822 0.3814 0.0715 0.1667 0.2630 0.1667 0.3752 0.0856 0.1214 0.0 0.0 0.0 5.6522 0.1417 2.9939 5.2445 0.0264 1.8045 0.0 2.7661 23.6230 0.0 0.0 0.0 0.0 0.0 0.0 0.0778 1.1506 5.9247 0.0878 3.3604 7.7421 1.1506 1.1265 5.0108 0.1013 2.4278 0.0 2.4890 41.7080 NaN NaN 0.0 0.0142 0.0230 0.0768 0.0729 0.0143 0.0513 0.0399 0.0365 1.2474 0.0017 NaN 0.0248 0.0005 46.3453 0.0069 677.1873 0.0 0.0053 0.0059 0.0081 0.0033 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0022 0.0013 0.0 0.0 0.0 0.0 NaN NaN NaN NaN 0.0049 0.0 65.0999 0.0002 1.1655 0.0068 0.0027 0.1921 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0120 10.5837 1.0323 4.3465 2.5939 3.2858 2.5197 15.0150 27.7464 0.0 5.5695 3.9300 9.0604 0.0000 368.9713 2.1196 6.1491 0.0 61.8918 3.1531 6.1188 1.4857 6.1911 2.8088 3.1595 10.4383 2.2655 8.4887 199.7866 8.6336 5.7093 1.6779 3.2153 48.5294 37.5793 16.4174 1.2364 1.9562 0.8123 1.0239 0.8340 1.5683 0.2645 0.2751 0.0 0.0 0.0 5.1072 4.3737 7.6142 2.2568 6.9233 4.7448 0.0 1.4336 40.4475 0.0 0.0 0.0 0.0 0.0 0.0 4.7415 463.2883 5.5652 3.0652 10.2211 73.5536 19.4865 13.2430 2.1627 30.8643 5.8042 0.0 1.2928 163.0249 0.0 0.0000 246.7762 0.0000 359.0444 130.6350 820.7900 194.4371 0.0000 58.1666 3.6822 NaN 3.2029 0.1441 6.6487 12.6788 23.6469 0.0 0.0000 0.0000 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 141.4365 0.0000 0.0 0.0 0.0 0.0 NaN NaN NaN NaN 1.6292 0.0 26.3970 0.0673 6.6475 3.1310 0.8832 8.8370 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.7910 2.9799 9.5796 0.1096 0.0078 0.0026 7.116 1.3526 408.798 74.640 0.7193 16.00 1.33 0.2829 7.1196 0.4989 53.1836 3.9139 1.7819 0.9634 0.1745 0.0375 18.1087 NaN NaN NaN NaN NaN NaN NaN NaN 535.0164 2.4335 5.92 0.2653 2.0111 0.0772 1.1065 10.9003 0.0096 0.0201 0.0060 208.2045 0.5019 0.0223 0.0055 4.4447 0.0096 0.0201 0.0060 208.2045 -1
2 2008-07-19 13:17:00 2932.61 2559.94 2186.4111 1698.0172 1.5102 100.0 95.4878 0.1241 1.4436 0.0041 0.0013 0.9615 202.0179 0.0 9.5157 416.7075 9.3144 0.9674 192.7035 12.5404 1.4123 -5447.75 2701.75 -4047.00 -1916.50 1.3122 2.0295 7.5788 67.1333 2.3333 0.1734 3.5986 84.7569 8.6590 50.1530 64.1114 49.8470 65.8389 84.7327 118.6128 14.37 5.434 70.0 364.3782 9.8783 131.8027 734.7924 1.2992 141.0845 1.0 637.2655 185.7574 0.0 4.486 4.748 2936.0 0.9139 0.9447 4.5873 23.8245 364.5364 10.1685 115.6273 11.3019 16.1755 24.2829 710.5095 0.8694 145.8000 1.0 625.9636 84.7681 140.6972 485.2665 0.0 -0.0078 -0.0326 -0.0052 0.0213 -0.0054 -0.1134 -0.0182 0.0287 7.1041 0.1362 NaN 2.4532 0.9880 1685.8514 0.1497 9317.1698 0.0553 0.0006 -0.0013 0.0000 0.0002 -0.1343 0.0 -0.1427 0.1218 0.0006 -0.0001 0.0134 -0.0026 -0.0016 -0.0006 0.0013 -0.0301 -0.0728 NaN NaN NaN 0.4684 0.9231 0.0 718.5777 0.9899 58.4808 0.6015 0.9772 6.4527 15.90 2.882 15.94 15.95 0.8798 3.094 0.4777 3.272 -0.1892 0.8194 0.9978 2.2592 998.4440 42.0579 89.0 126.4 96.5 45.1001 306.0380 0.3263 0.0 8.33 0.0038 0.0754 0.0483 0.0619 0.0221 8.2660 0.0 4.819 8.443 0.4909 0.0177 8.2054 0.47 0.0497 NaN NaN 562.0 788.0 759.0 2100.0 0.187 0.117 0.068 2.1 1.4 0.123 0.319 1.0824 0.0369 0.3141 0.5753 0.3141 0.9677 0.2706 0.326 0.0 0.0 17.78 0.745 13.31 22.912 0.1959 9.21 0.0 17.87 60.110 0.0 0.0 0.0 0.0 0.0 0.0 0.139 5.09 19.75 0.949 9.71 16.73 5.09 11.059 22.624 0.1164 13.30 0.0 16.73 79.618 0.0 0.0339 0.0494 0.0696 0.0406 0.0401 0.0840 0.0349 0.0718 2.4266 0.0014 NaN 0.0963 0.0152 182.4956 0.0284 839.6006 0.0 0.0192 0.0170 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0062 0.0040 0.0 0.0 0.0 0.0 NaN NaN NaN 0.1729 0.0273 0.0 104.4042 0.0007 4.1446 0.0733 0.0063 0.4166 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0487 29.621 3.9133 23.5510 41.3837 32.6256 15.7716 97.3868 0.1117 0.0 2.5274 0.0012 0.0249 0.0152 0.0157 0.0075 2.8705 0.0 1.5306 2.5493 0.1479 0.0059 2.8046 0.1185 0.0167 NaN NaN 251.4536 329.6406 325.0672 902.4576 0.0800 0.0583 0.0326 0.6964 0.4031 0.0416 0.1041 0.3846 0.0151 0.1288 0.2268 0.1288 0.3677 0.1175 0.1261 0.0 0.0 0.0 5.7247 0.2682 3.8541 6.1797 0.0546 2.5680 0.0 4.6067 16.0104 0.0 0.0 0.0 0.0 0.0 0.0 0.0243 1.5481 5.9453 0.2777 3.1600 8.9855 1.5481 2.9844 6.2277 0.0353 3.7663 0.0 5.6983 24.7959 13.5664 15.4488 0.0 0.0105 0.0208 0.0327 0.0171 0.0116 0.0428 0.0154 0.0383 0.7786 0.0005 NaN 0.0302 0.0046 58.0575 0.0092 283.6616 0.0 0.0054 0.0043 0.0030 0.0037 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0021 0.0015 0.0 0.0 0.0 0.0 NaN NaN NaN 0.0221 0.0100 0.0 28.7334 0.0003 1.2356 0.0190 0.0020 0.1375 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0190 11.4871 1.1798 4.0782 4.3102 3.7696 2.0627 18.0233 21.6062 0.0 8.7236 3.0609 5.2231 0.0000 0.0000 2.2943 4.0917 0.0 50.6425 2.0261 5.2707 1.8268 4.2581 3.7479 3.5220 10.3162 29.1663 18.7546 109.5747 14.2503 5.7650 0.8972 3.1281 60.0000 70.9161 8.8647 1.2771 0.4264 0.6263 0.8973 0.6301 1.4698 0.3194 0.2748 0.0 0.0 0.0 4.8795 7.5418 10.0984 3.1182 15.0790 6.5280 0.0 2.8042 32.3594 0.0 0.0 0.0 0.0 0.0 0.0 3.0301 21.3645 5.4178 9.3327 8.3977 148.0287 31.4674 45.5423 3.1842 13.3923 9.1221 0.0 2.6727 93.9245 0.0 434.2674 151.7665 0.0000 190.3869 746.9150 74.0741 191.7582 250.1742 34.1573 1.0281 NaN 3.9238 1.5357 10.8251 18.9849 9.0113 0.0 0.0000 0.0000 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 240.7767 244.2748 0.0 0.0 0.0 0.0 NaN NaN NaN 36.9067 2.9626 0.0 14.5293 0.0751 7.0870 12.1831 0.6451 6.4568 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.1538 2.9667 9.3046 0.1096 0.0078 0.0026 7.116 0.7942 411.136 74.654 0.1832 16.16 0.85 0.0857 7.1619 0.3752 23.0713 3.9306 1.1386 1.5021 0.3718 0.1233 24.7524 267.064 0.9032 1.10 0.6219 0.4122 0.2562 0.4119 68.8489 535.0245 2.0293 11.21 0.1882 4.0923 0.0640 2.0952 9.2721 0.0584 0.0484 0.0148 82.8602 0.4958 0.0157 0.0039 3.1745 0.0584 0.0484 0.0148 82.8602 1
3 2008-07-19 14:43:00 2988.72 2479.90 2199.0333 909.7926 1.3204 100.0 104.2367 0.1217 1.4882 -0.0124 -0.0033 0.9629 201.8482 0.0 9.6052 422.2894 9.6924 0.9687 192.1557 12.4782 1.4011 -5468.25 2648.25 -4515.00 -1657.25 1.3137 2.0038 7.3145 62.9333 2.6444 0.2071 3.3813 84.9105 8.6789 50.5100 64.1125 49.4900 65.1951 86.6867 117.0442 76.90 1.279 70.0 363.0273 9.9305 131.8027 733.8778 1.3027 142.5427 1.0 637.3727 189.9079 0.0 4.486 4.748 2936.0 0.9139 0.9447 4.5873 24.3791 361.4582 10.2112 116.1818 13.5597 15.6209 23.4736 710.4043 0.9761 147.6545 1.0 625.2945 70.2289 160.3210 464.9735 0.0 -0.0555 -0.0461 -0.0400 0.0400 0.0676 -0.1051 0.0028 0.0277 7.5925 0.1302 NaN 2.4004 0.9904 1752.0968 0.1958 8205.7000 0.0697 -0.0003 -0.0021 -0.0001 0.0002 0.0411 0.0 0.0177 -0.0195 -0.0002 0.0000 -0.0699 -0.0059 0.0003 0.0003 0.0021 -0.0483 -0.1180 NaN NaN NaN 0.4647 0.9564 0.0 709.0867 0.9906 58.6635 0.6016 0.9761 6.4935 15.55 3.132 15.61 15.59 1.3660 2.480 0.5176 3.119 0.2838 0.7244 0.9961 2.3802 980.4510 41.1025 127.0 118.0 123.7 47.8000 162.4320 0.1915 0.0 5.51 0.0030 0.1140 0.0393 0.0613 0.0190 13.2651 0.0 9.073 15.241 1.3029 0.0150 11.9738 0.35 0.0699 NaN NaN 859.0 355.0 3433.0 3004.0 0.068 0.108 0.100 1.7 0.9 0.086 0.241 0.9386 0.0356 0.2618 0.4391 0.2618 0.8567 0.2452 0.390 0.0 0.0 16.22 0.693 14.67 22.562 0.1786 5.69 0.0 18.20 52.571 0.0 0.0 0.0 0.0 0.0 0.0 0.139 5.92 23.60 1.264 10.63 13.56 5.92 11.382 24.320 0.3458 9.56 0.0 21.97 104.950 0.0 0.1248 0.0463 0.1223 0.0354 0.0708 0.0754 0.0643 0.0932 5.5398 0.0023 NaN 0.0764 0.0015 152.0885 0.0573 820.3999 0.0 0.0152 0.0149 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0067 0.0040 0.0 0.0 0.0 0.0 NaN NaN NaN 0.0191 0.0234 0.0 94.0954 0.0010 3.2119 0.0406 0.0072 0.4212 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0513 31.830 3.1959 33.8960 37.8477 44.3906 16.9347 50.3631 0.0581 0.0 2.1775 0.0007 0.0417 0.0115 0.0172 0.0063 4.2154 0.0 2.8960 4.0526 0.3882 0.0049 3.9403 0.0916 0.0245 NaN NaN 415.5048 157.0889 1572.6896 1377.4276 0.0285 0.0445 0.0465 0.6305 0.3046 0.0286 0.0824 0.3483 0.0128 0.1004 0.1701 0.1004 0.3465 0.0973 0.1675 0.0 0.0 0.0 5.4440 0.2004 4.1900 6.3329 0.0479 1.7339 0.0 4.9660 15.7375 0.0 0.0 0.0 0.0 0.0 0.0 0.0243 1.7317 6.6262 0.3512 3.2699 9.4020 1.7317 3.0672 6.6839 0.0928 3.0229 0.0 6.3292 29.0339 8.4026 4.8851 0.0 0.0407 0.0198 0.0531 0.0167 0.0224 0.0422 0.0273 0.0484 1.8222 0.0006 NaN 0.0252 0.0004 45.7058 0.0188 309.8492 0.0 0.0046 0.0049 0.0028 0.0034 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0024 0.0014 0.0 0.0 0.0 0.0 NaN NaN NaN 0.0038 0.0068 0.0 32.4228 0.0003 1.1135 0.0132 0.0023 0.1348 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0155 13.3972 1.1907 5.6363 3.9482 4.9881 2.1737 17.8537 14.5054 0.0 5.2860 2.4643 7.6602 317.7362 0.0000 1.9689 6.5718 0.0 94.4594 3.6091 13.4420 1.5441 6.2313 2.8049 4.9898 15.7089 13.4051 76.0354 181.2641 5.1760 5.3899 1.3671 2.7013 34.0336 41.5236 7.1274 1.1054 0.4097 0.5183 0.6849 0.5290 1.3141 0.2829 0.3332 0.0 0.0 0.0 4.4680 6.9785 11.1303 3.0744 13.7105 3.9918 0.0 2.8555 27.6824 0.0 0.0 0.0 0.0 0.0 0.0 3.0301 24.2831 6.5291 12.3786 9.1494 100.0021 37.8979 48.4887 3.4234 35.4323 6.4746 0.0 3.5135 149.4399 0.0 225.0169 100.4883 305.7500 88.5553 104.6660 71.7583 0.0000 336.7660 72.9635 1.7670 NaN 3.1817 0.1488 8.6804 29.2542 9.9979 0.0 0.0000 711.6418 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 113.5593 0.0000 0.0 0.0 0.0 0.0 NaN NaN NaN 4.1200 2.4416 0.0 13.2699 0.0977 5.4751 6.7553 0.7404 6.4865 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.1565 3.2465 7.7754 0.1096 0.0078 0.0026 7.116 1.1650 372.822 72.442 1.8804 131.68 39.33 0.6812 56.9303 17.4781 161.4081 35.3198 54.2917 1.1613 0.7288 0.2710 62.7572 268.228 0.6511 7.32 0.1630 3.5611 0.0670 2.7290 25.0363 530.5682 2.0253 9.33 0.1738 2.8971 0.0525 1.7585 8.5831 0.0202 0.0149 0.0044 73.8432 0.4990 0.0103 0.0025 2.0544 0.0202 0.0149 0.0044 73.8432 -1
4 2008-07-19 15:22:00 3032.24 2502.87 2233.3667 1326.5200 1.5334 100.0 100.3967 0.1235 1.5031 -0.0031 -0.0072 0.9569 201.9424 0.0 10.5661 420.5925 10.3387 0.9735 191.6037 12.4735 1.3888 -5476.25 2635.25 -3987.50 117.00 1.2887 1.9912 7.2748 62.8333 3.1556 0.2696 3.2728 86.3269 8.7677 50.2480 64.1511 49.7520 66.1542 86.1468 121.4364 76.39 2.209 70.0 353.3400 10.4091 176.3136 789.7523 1.0341 138.0882 1.0 667.7418 233.5491 0.0 4.624 4.894 2865.0 0.9298 0.9449 4.6414 -12.2945 355.0809 9.7948 144.0191 21.9782 32.2945 44.1498 745.6025 0.9256 146.6636 1.0 645.7636 65.8417 NaN NaN 0.0 -0.0534 0.0183 -0.0167 -0.0449 0.0034 -0.0178 -0.0123 -0.0048 7.5017 0.1342 NaN 2.4530 0.9902 1828.3846 0.1829 9014.4600 0.0448 -0.0077 -0.0001 -0.0001 -0.0001 0.2189 0.0 -0.6704 -0.0167 0.0004 -0.0003 0.0696 -0.0045 0.0002 0.0078 0.0000 -0.0799 -0.2038 NaN NaN NaN NaN 0.9424 0.0 796.5950 0.9908 58.3858 0.5913 0.9628 6.3551 15.75 3.148 15.73 15.71 0.9460 3.027 0.5328 3.299 -0.5677 0.7780 1.0010 2.3715 993.1274 38.1448 119.0 143.2 123.1 48.8000 296.3030 0.3744 0.0 3.64 0.0041 0.0634 0.0451 0.0623 0.0240 14.2354 0.0 9.005 12.506 0.4434 0.0126 13.9047 0.43 0.0538 NaN NaN 699.0 283.0 1747.0 1443.0 0.147 0.040 0.113 3.9 0.8 0.101 0.499 0.5760 0.0631 0.3053 0.5830 0.3053 0.8285 0.1308 0.922 0.0 0.0 15.24 0.282 10.85 37.715 0.1189 3.98 0.0 25.54 72.149 0.0 0.0 0.0 0.0 0.0 0.0 0.250 5.52 15.76 0.519 10.71 19.77 5.52 8.446 33.832 0.3951 9.09 0.0 19.77 92.307 0.0 0.0915 0.0506 0.0769 0.1079 0.0797 0.1047 0.0924 0.1015 4.1338 0.0030 NaN 0.0802 0.0004 69.1510 0.1970 1406.4004 0.0 0.0227 0.0272 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0067 0.0031 0.0 0.0 0.0 0.0 NaN NaN NaN NaN 0.0240 0.0 149.2172 0.0006 2.5775 0.0177 0.0214 0.4051 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0488 19.862 3.6163 34.1250 55.9626 53.0876 17.4864 88.7672 0.1092 0.0 1.0929 0.0013 0.0257 0.0116 0.0163 0.0080 4.4239 0.0 3.2376 3.6536 0.1293 0.0040 4.3474 0.1275 0.0181 NaN NaN 319.1252 128.0296 799.5884 628.3083 0.0755 0.0181 0.0476 1.3500 0.2698 0.0320 0.1541 0.2155 0.0310 0.1354 0.2194 0.1354 0.3072 0.0582 0.3574 0.0 0.0 0.0 4.8956 0.0766 2.9130 11.0583 0.0327 1.1229 0.0 7.3296 23.1160 0.0 0.0 0.0 0.0 0.0 0.0 0.0822 1.6216 4.7279 0.1773 3.1550 9.7777 1.6216 2.5923 10.5352 0.1301 3.0939 0.0 6.3767 32.0537 NaN NaN 0.0 0.0246 0.0221 0.0329 0.0522 0.0256 0.0545 0.0476 0.0463 1.5530 0.0010 NaN 0.0286 0.0001 21.0312 0.0573 494.7368 0.0 0.0063 0.0077 0.0052 0.0027 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0025 0.0012 0.0 0.0 0.0 0.0 NaN NaN NaN NaN 0.0089 0.0 57.2692 0.0002 0.8495 0.0065 0.0077 0.1356 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0165 7.1493 1.1704 5.3823 4.7226 4.9184 2.1850 22.3369 24.4142 0.0 3.6256 3.3208 4.2178 0.0000 866.0295 2.5046 7.0492 0.0 85.2255 2.9734 4.2892 1.2943 7.2570 3.4473 3.8754 12.7642 10.7390 43.8119 0.0000 11.4064 2.0088 1.5533 6.2069 25.3521 37.4691 15.2470 0.6672 0.7198 0.6076 0.9088 0.6136 1.2524 0.1518 0.7592 0.0 0.0 0.0 4.3131 2.7092 6.1538 4.7756 11.4945 2.8822 0.0 3.8248 30.8924 0.0 0.0 0.0 0.0 0.0 0.0 5.3863 44.8980 4.4384 5.2987 7.4365 89.9529 17.0927 19.1303 4.5375 42.6838 6.1979 0.0 3.0615 140.1953 0.0 171.4486 276.8810 461.8619 240.1781 0.0000 587.3773 748.1781 0.0000 55.1057 2.2358 NaN 3.2712 0.0372 3.7821 107.6905 15.6016 0.0 293.1396 0.0000 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 148.0663 0.0000 0.0 0.0 0.0 0.0 NaN NaN NaN NaN 2.5512 0.0 18.7319 0.0616 4.4146 2.9954 2.2181 6.3745 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.0579 1.9999 9.4805 0.1096 0.0078 0.0026 7.116 1.4636 399.914 79.156 1.0388 19.63 1.98 0.4287 9.7608 0.8311 70.9706 4.9086 2.5014 0.9778 0.2156 0.0461 22.0500 NaN NaN NaN NaN NaN NaN NaN NaN 532.0155 2.0275 8.83 0.2224 3.1776 0.0706 1.6597 10.9698 NaN NaN NaN NaN 0.4800 0.4766 0.1045 99.3032 0.0202 0.0149 0.0044 73.8432 -1
In [5]:
Data.isnull().sum().sum()
# we can see that total of 41951 data is missing in entire data set
Out[5]:
41951
In [6]:
Data.info()
# We can see that we have float64(590), int64(1), object(1) data types in our data set
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 1567 entries, 0 to 1566
Columns: 592 entries, Time to Pass/Fail
dtypes: float64(590), int64(1), object(1)
memory usage: 7.1+ MB
In [7]:
Data.isnull().sum()
Out[7]:
Time            0
0               6
1               7
2              14
3              14
4              14
5              14
6              14
7               9
8               2
9               2
10              2
11              2
12              2
13              3
14              3
15              3
16              3
17              3
18              3
19             10
20              0
21              2
22              2
23              2
24              2
25              2
26              2
27              2
28              2
29              2
30              2
31              2
32              1
33              1
34              1
35              1
36              1
37              1
38              1
39              1
40             24
41             24
42              1
43              1
44              1
45              1
46              1
47              1
48              1
49              1
50              1
51              1
52              1
53              4
54              4
55              4
56              4
57              4
58              4
59              7
60              6
61              6
62              6
63              7
64              7
65              7
66              6
67              6
68              6
69              6
70              6
71              6
72            794
73            794
74              6
75             24
76             24
77             24
78             24
79             24
80             24
81             24
82             24
83              1
84             12
85           1341
86              0
87              0
88              0
89             51
90             51
91              6
92              2
93              2
94              6
95              6
96              6
97              6
98              6
99              6
100             6
101             6
102             6
103             2
104             2
105             6
106             6
107             6
108             6
109          1018
110          1018
111          1018
112           715
113             0
114             0
115             0
116             0
117             0
118            24
119             0
120             0
121             9
122             9
123             9
124             9
125             9
126             9
127             9
128             9
129             9
130             9
131             9
132             8
133             8
134             8
135             5
136             6
137             7
138            14
139            14
140            14
141            14
142            14
143             9
144             2
145             2
146             2
147             2
148             2
149             3
150             3
151             3
152             3
153             3
154             3
155            10
156             0
157          1429
158          1429
159             2
160             2
161             2
162             2
163             2
164             2
165             2
166             2
167             2
168             2
169             2
170             1
171             1
172             1
173             1
174             1
175             1
176             1
177             1
178            24
179             1
180             1
181             1
182             1
183             1
184             1
185             1
186             1
187             1
188             1
189             1
190             4
191             4
192             4
193             4
194             4
195             4
196             7
197             6
198             6
199             6
200             7
201             7
202             7
203             6
204             6
205             6
206             6
207             6
208             6
209             6
210            24
211            24
212            24
213            24
214            24
215            24
216            24
217            24
218             1
219            12
220          1341
221             0
222             0
223             0
224            51
225            51
226             6
227             2
228             2
229             6
230             6
231             6
232             6
233             6
234             6
235             6
236             6
237             6
238             2
239             2
240             6
241             6
242             6
243             6
244          1018
245          1018
246          1018
247           715
248             0
249             0
250             0
251             0
252             0
253            24
254             0
255             0
256             9
257             9
258             9
259             9
260             9
261             9
262             9
263             9
264             9
265             9
266             9
267             8
268             8
269             8
270             5
271             6
272             7
273            14
274            14
275            14
276            14
277            14
278             9
279             2
280             2
281             2
282             2
283             2
284             3
285             3
286             3
287             3
288             3
289             3
290            10
291             0
292          1429
293          1429
294             2
295             2
296             2
297             2
298             2
299             2
300             2
301             2
302             2
303             2
304             2
305             1
306             1
307             1
308             1
309             1
310             1
311             1
312             1
313            24
314            24
315             1
316             1
317             1
318             1
319             1
320             1
321             1
322             1
323             1
324             1
325             1
326             4
327             4
328             4
329             4
330             4
331             4
332             7
333             6
334             6
335             6
336             7
337             7
338             7
339             6
340             6
341             6
342             6
343             6
344             6
345           794
346           794
347             6
348            24
349            24
350            24
351            24
352            24
353            24
354            24
355            24
356             1
357            12
358          1341
359             0
360             0
361             0
362            51
363            51
364             6
365             2
366             2
367             6
368             6
369             6
370             6
371             6
372             6
373             6
374             6
375             6
376             2
377             2
378             6
379             6
380             6
381             6
382          1018
383          1018
384          1018
385           715
386             0
387             0
388             0
389             0
390             0
391            24
392             0
393             0
394             9
395             9
396             9
397             9
398             9
399             9
400             9
401             9
402             9
403             9
404             9
405             8
406             8
407             8
408             5
409             6
410             7
411            14
412            14
413            14
414            14
415            14
416             9
417             2
418             2
419             2
420             2
421             2
422             3
423             3
424             3
425             3
426             3
427             3
428            10
429             0
430             2
431             2
432             2
433             2
434             2
435             2
436             2
437             2
438             2
439             2
440             2
441             1
442             1
443             1
444             1
445             1
446             1
447             1
448             1
449            24
450            24
451             1
452             1
453             1
454             1
455             1
456             1
457             1
458             1
459             1
460             1
461             1
462             4
463             4
464             4
465             4
466             4
467             4
468             7
469             6
470             6
471             6
472             7
473             7
474             7
475             6
476             6
477             6
478             6
479             6
480             6
481             6
482            24
483            24
484            24
485            24
486            24
487            24
488            24
489            24
490             1
491            12
492          1341
493             0
494             0
495             0
496            51
497            51
498             6
499             2
500             2
501             6
502             6
503             6
504             6
505             6
506             6
507             6
508             6
509             6
510             2
511             2
512             6
513             6
514             6
515             6
516          1018
517          1018
518          1018
519           715
520             0
521             0
522             0
523             0
524             0
525            24
526             0
527             0
528             9
529             9
530             9
531             9
532             9
533             9
534             9
535             9
536             9
537             9
538             9
539             8
540             8
541             8
542             2
543             2
544             2
545             2
546           260
547           260
548           260
549           260
550           260
551           260
552           260
553           260
554           260
555           260
556           260
557           260
558             1
559             1
560             1
561             1
562           273
563           273
564           273
565           273
566           273
567           273
568           273
569           273
570             0
571             0
572             0
573             0
574             0
575             0
576             0
577             0
578           949
579           949
580           949
581           949
582             1
583             1
584             1
585             1
586             1
587             1
588             1
589             1
Pass/Fail       0
dtype: int64
In [8]:
# We can see that many columns have too many null values, so columns which have null values more than 70% can be droppped
# as majority of the data is missing imputing and creating majority of the artificial data is of no use in above case
# SO columns having null values more than roughly 1000 can be dropped
counter  = 0

for columns in Data.columns:
    if Data[columns].isnull().sum() >= 1000:
        counter = counter + 1
        print( columns , 'Column has', Data[columns].isnull().sum() , ' null values, hence can be dropped')
        del Data[columns]
        

print('New shape of the data set after deleting above', counter ,' columns is', Data.shape)
85 Column has 1341  null values, hence can be dropped
109 Column has 1018  null values, hence can be dropped
110 Column has 1018  null values, hence can be dropped
111 Column has 1018  null values, hence can be dropped
157 Column has 1429  null values, hence can be dropped
158 Column has 1429  null values, hence can be dropped
220 Column has 1341  null values, hence can be dropped
244 Column has 1018  null values, hence can be dropped
245 Column has 1018  null values, hence can be dropped
246 Column has 1018  null values, hence can be dropped
292 Column has 1429  null values, hence can be dropped
293 Column has 1429  null values, hence can be dropped
358 Column has 1341  null values, hence can be dropped
382 Column has 1018  null values, hence can be dropped
383 Column has 1018  null values, hence can be dropped
384 Column has 1018  null values, hence can be dropped
492 Column has 1341  null values, hence can be dropped
516 Column has 1018  null values, hence can be dropped
517 Column has 1018  null values, hence can be dropped
518 Column has 1018  null values, hence can be dropped
New shape of the data set after deleting above 20  columns is (1567, 572)
In [9]:
# we wont be requiring time column to classify condutor into pass or fail category, hence we can drop time column too
Data.drop(labels = 'Time', axis = 1, inplace = True)
Data.shape
Out[9]:
(1567, 571)
In [10]:
Data.describe().T
Out[10]:
count mean std min 25% 50% 75% max
0 1561.0 3014.452896 73.621787 2743.2400 2966.260000 3011.49000 3056.650000 3356.3500
1 1560.0 2495.850231 80.407705 2158.7500 2452.247500 2499.40500 2538.822500 2846.4400
2 1553.0 2200.547318 29.513152 2060.6600 2181.044400 2201.06670 2218.055500 2315.2667
3 1553.0 1396.376627 441.691640 0.0000 1081.875800 1285.21440 1591.223500 3715.0417
4 1553.0 4.197013 56.355540 0.6815 1.017700 1.31680 1.525700 1114.5366
5 1553.0 100.000000 0.000000 100.0000 100.000000 100.00000 100.000000 100.0000
6 1553.0 101.112908 6.237214 82.1311 97.920000 101.51220 104.586700 129.2522
7 1558.0 0.121822 0.008961 0.0000 0.121100 0.12240 0.123800 0.1286
8 1565.0 1.462862 0.073897 1.1910 1.411200 1.46160 1.516900 1.6564
9 1565.0 -0.000841 0.015116 -0.0534 -0.010800 -0.00130 0.008400 0.0749
10 1565.0 0.000146 0.009302 -0.0349 -0.005600 0.00040 0.005900 0.0530
11 1565.0 0.964353 0.012452 0.6554 0.958100 0.96580 0.971300 0.9848
12 1565.0 199.956809 3.257276 182.0940 198.130700 199.53560 202.007100 272.0451
13 1564.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
14 1564.0 9.005371 2.796596 2.2493 7.094875 8.96700 10.861875 19.5465
15 1564.0 413.086035 17.221095 333.4486 406.127400 412.21910 419.089275 824.9271
16 1564.0 9.907603 2.403867 4.4696 9.567625 9.85175 10.128175 102.8677
17 1564.0 0.971444 0.012062 0.5794 0.968200 0.97260 0.976800 0.9848
18 1564.0 190.047354 2.781041 169.1774 188.299825 189.66420 192.189375 215.5977
19 1557.0 12.481034 0.217965 9.8773 12.460000 12.49960 12.547100 12.9898
20 1567.0 1.405054 0.016737 1.1797 1.396500 1.40600 1.415000 1.4534
21 1565.0 -5618.393610 626.822178 -7150.2500 -5933.250000 -5523.25000 -5356.250000 0.0000
22 1565.0 2699.378435 295.498535 0.0000 2578.000000 2664.00000 2841.750000 3656.2500
23 1565.0 -3806.299734 1380.162148 -9986.7500 -4371.750000 -3820.75000 -3352.750000 2363.0000
24 1565.0 -298.598136 2902.690117 -14804.5000 -1476.000000 -78.75000 1377.250000 14106.0000
25 1565.0 1.203845 0.177600 0.0000 1.094800 1.28300 1.304300 1.3828
26 1565.0 1.938477 0.189495 0.0000 1.906500 1.98650 2.003200 2.0528
27 1565.0 6.638628 1.244249 0.0000 5.263700 7.26470 7.329700 7.6588
28 1565.0 69.499532 3.461181 59.4000 67.377800 69.15560 72.266700 77.9000
29 1565.0 2.366197 0.408694 0.6667 2.088900 2.37780 2.655600 3.5111
30 1565.0 0.184159 0.032944 0.0341 0.161700 0.18670 0.207100 0.2851
31 1565.0 3.673189 0.535322 2.0698 3.362700 3.43100 3.531300 4.8044
32 1566.0 85.337469 2.026549 83.1829 84.490500 85.13545 85.741900 105.6038
33 1566.0 8.960279 1.344456 7.6032 8.580000 8.76980 9.060600 23.3453
34 1566.0 50.582639 1.182618 49.8348 50.252350 50.39640 50.578800 59.7711
35 1566.0 64.555787 2.574749 63.6774 64.024800 64.16580 64.344700 94.2641
36 1566.0 49.417370 1.182619 40.2289 49.421200 49.60360 49.747650 50.1652
37 1566.0 66.221274 0.304141 64.9193 66.040650 66.23180 66.343275 67.9586
38 1566.0 86.836577 0.446756 84.7327 86.578300 86.82070 87.002400 88.4188
39 1566.0 118.679554 1.807221 111.7128 118.015600 118.39930 118.939600 133.3898
40 1543.0 67.904909 24.062943 1.4340 74.800000 78.29000 80.200000 86.1200
41 1543.0 3.353066 2.360425 -0.0759 2.690000 3.07400 3.521000 37.8800
42 1566.0 70.000000 0.000000 70.0000 70.000000 70.00000 70.000000 70.0000
43 1566.0 355.538904 6.234706 342.7545 350.801575 353.72090 360.772250 377.2973
44 1566.0 10.031165 0.175038 9.4640 9.925425 10.03485 10.152475 11.0530
45 1566.0 136.743060 7.849247 108.8464 130.728875 136.40000 142.098225 176.3136
46 1566.0 733.672811 12.170315 699.8139 724.442300 733.45000 741.454500 789.7523
47 1566.0 1.177958 0.189637 0.4967 0.985000 1.25105 1.340350 1.5111
48 1566.0 139.972231 4.524251 125.7982 136.926800 140.00775 143.195700 163.2509
49 1566.0 1.000000 0.000000 1.0000 1.000000 1.00000 1.000000 1.0000
50 1566.0 632.254197 8.643985 607.3927 625.928425 631.37090 638.136325 667.7418
51 1566.0 157.420991 60.925108 40.2614 115.508975 183.31815 206.977150 258.5432
52 1566.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
53 1563.0 4.592971 0.054950 3.7060 4.574000 4.59600 4.617000 4.7640
54 1563.0 4.838523 0.059581 3.9320 4.816000 4.84300 4.869000 5.0110
55 1563.0 2856.172105 25.749317 2801.0000 2836.000000 2854.00000 2874.000000 2936.0000
56 1563.0 0.928849 0.006807 0.8755 0.925450 0.93100 0.933100 0.9378
57 1563.0 0.949215 0.004176 0.9319 0.946650 0.94930 0.952000 0.9598
58 1563.0 4.593312 0.085095 4.2199 4.531900 4.57270 4.668600 4.8475
59 1560.0 2.960241 9.532220 -28.9882 -1.871575 0.94725 4.385225 168.1455
60 1561.0 355.159094 6.027889 324.7145 350.596400 353.79910 359.673600 373.8664
61 1561.0 10.423143 0.274877 9.4611 10.283000 10.43670 10.591600 11.7849
62 1561.0 116.502329 8.629022 81.4900 112.022700 116.21180 120.927300 287.1509
63 1560.0 13.989927 7.119863 1.6591 10.364300 13.24605 16.376100 188.0923
64 1560.0 20.542109 4.977467 6.4482 17.364800 20.02135 22.813625 48.9882
65 1560.0 27.131816 7.121703 4.3080 23.056425 26.26145 29.914950 118.0836
66 1561.0 706.668523 11.623078 632.4226 698.770200 706.45360 714.597000 770.6084
67 1561.0 16.715444 307.502293 0.4137 0.890700 0.97830 1.065000 7272.8283
68 1561.0 147.437578 4.240095 87.0255 145.237300 147.59730 149.959100 167.8309
69 1561.0 1.000000 0.000000 1.0000 1.000000 1.00000 1.000000 1.0000
70 1561.0 619.101687 9.539190 581.7773 612.774500 619.03270 625.170000 722.6018
71 1561.0 104.329033 31.651899 21.4332 87.484200 102.60430 115.498900 238.4775
72 773.0 150.361552 18.388481 -59.4777 145.305300 152.29720 158.437800 175.4132
73 773.0 468.020404 17.629886 456.0447 464.458100 466.08170 467.889900 692.4256
74 1561.0 0.002688 0.106190 0.0000 0.000000 0.00000 0.000000 4.1955
75 1543.0 -0.006903 0.022292 -0.1049 -0.019550 -0.00630 0.007100 0.2315
76 1543.0 -0.029390 0.033203 -0.1862 -0.051900 -0.02890 -0.006500 0.0723
77 1543.0 -0.007041 0.031368 -0.1046 -0.029500 -0.00990 0.009250 0.1331
78 1543.0 -0.013643 0.047872 -0.3482 -0.047600 -0.01250 0.012200 0.2492
79 1543.0 0.003458 0.023080 -0.0568 -0.010800 0.00060 0.013200 0.1013
80 1543.0 -0.018531 0.049226 -0.1437 -0.044500 -0.00870 0.009100 0.1186
81 1543.0 -0.021153 0.017021 -0.0982 -0.027200 -0.01960 -0.012000 0.0584
82 1543.0 0.006055 0.036074 -0.2129 -0.018000 0.00760 0.026900 0.1437
83 1566.0 7.452067 0.516251 5.8257 7.104225 7.46745 7.807625 8.9904
84 1555.0 0.133108 0.005051 0.1174 0.129800 0.13300 0.136300 0.1505
86 1567.0 2.401872 0.037332 2.2425 2.376850 2.40390 2.428600 2.5555
87 1567.0 0.982420 0.012848 0.7749 0.975800 0.98740 0.989700 0.9935
88 1567.0 1807.815021 53.537262 1627.4714 1777.470300 1809.24920 1841.873000 2105.1823
89 1516.0 0.188703 0.052373 0.1113 0.169375 0.19010 0.200425 1.4727
90 1516.0 8827.536865 396.313662 7397.3100 8564.689975 8825.43510 9065.432400 10746.6000
91 1561.0 0.002440 0.087683 -0.3570 -0.042900 0.00000 0.050700 0.3627
92 1565.0 0.000507 0.003231 -0.0126 -0.001200 0.00040 0.002000 0.0281
93 1565.0 -0.000541 0.003010 -0.0171 -0.001600 -0.00020 0.001000 0.0133
94 1561.0 -0.000029 0.000174 -0.0020 -0.000100 0.00000 0.000100 0.0011
95 1561.0 0.000060 0.000104 -0.0009 0.000000 0.00000 0.000100 0.0009
96 1561.0 0.017127 0.219578 -1.4803 -0.088600 0.00390 0.122000 2.5093
97 1561.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
98 1561.0 -0.018143 0.427110 -5.2717 -0.218800 0.00000 0.189300 2.5698
99 1561.0 0.001540 0.062740 -0.5283 -0.029800 0.00000 0.029800 0.8854
100 1561.0 -0.000021 0.000356 -0.0030 -0.000200 0.00000 0.000200 0.0023
101 1561.0 -0.000007 0.000221 -0.0024 -0.000100 0.00000 0.000100 0.0017
102 1561.0 0.001115 0.062968 -0.5353 -0.035700 0.00000 0.033600 0.2979
103 1565.0 -0.009789 0.003065 -0.0329 -0.011800 -0.01010 -0.008200 0.0203
104 1565.0 -0.000015 0.000851 -0.0119 -0.000400 0.00000 0.000400 0.0071
105 1561.0 -0.000498 0.003202 -0.0281 -0.001900 -0.00020 0.001100 0.0127
106 1561.0 0.000540 0.002988 -0.0133 -0.001000 0.00020 0.001600 0.0172
107 1561.0 -0.001766 0.087475 -0.5226 -0.048600 0.00000 0.049000 0.4856
108 1561.0 -0.010789 0.086758 -0.3454 -0.064900 -0.01120 0.038000 0.3938
112 852.0 0.457538 0.048939 0.0000 0.459300 0.46285 0.466425 0.4885
113 1567.0 0.945424 0.012133 0.8534 0.938600 0.94640 0.952300 0.9763
114 1567.0 0.000123 0.001668 0.0000 0.000000 0.00000 0.000000 0.0414
115 1567.0 747.383792 48.949250 544.0254 721.023000 750.86140 776.781850 924.5318
116 1567.0 0.987130 0.009497 0.8900 0.989500 0.99050 0.990900 0.9924
117 1567.0 58.625908 6.485174 52.8068 57.978300 58.54910 59.133900 311.7344
118 1543.0 0.598412 0.008102 0.5274 0.594100 0.59900 0.603400 0.6245
119 1567.0 0.970777 0.008949 0.8411 0.964800 0.96940 0.978300 0.9827
120 1567.0 6.310863 0.124304 5.1259 6.246400 6.31360 6.375850 7.5220
121 1558.0 15.796425 0.099618 15.4600 15.730000 15.79000 15.860000 16.0700
122 1558.0 3.898390 0.904120 1.6710 3.202000 3.87700 4.392000 6.8890
123 1558.0 15.829660 0.108315 15.1700 15.762500 15.83000 15.900000 16.1000
124 1558.0 15.794705 0.114144 15.4300 15.722500 15.78000 15.870000 16.1000
125 1558.0 1.184956 0.280555 0.3122 0.974400 1.14400 1.338000 2.4650
126 1558.0 2.750728 0.253471 2.3400 2.572000 2.73500 2.873000 3.9910
127 1558.0 0.648478 0.135409 0.3161 0.548900 0.65390 0.713500 1.1750
128 1558.0 3.192182 0.264175 0.0000 3.074000 3.19500 3.311000 3.8950
129 1558.0 -0.554228 1.220479 -3.7790 -0.898800 -0.14190 0.047300 2.4580
130 1558.0 0.744976 0.082531 0.4199 0.688700 0.75875 0.814500 0.8884
131 1558.0 0.997808 0.002251 0.9936 0.996400 0.99775 0.998900 1.0190
132 1559.0 2.318545 0.053181 2.1911 2.277300 2.31240 2.358300 2.4723
133 1559.0 1004.043093 6.537701 980.4510 999.996100 1004.05000 1008.670600 1020.9944
134 1559.0 39.391979 2.990476 33.3658 37.347250 38.90260 40.804600 64.1287
135 1562.0 117.960948 57.544627 58.0000 92.000000 109.00000 127.000000 994.0000
136 1561.0 138.194747 53.909792 36.1000 90.000000 134.60000 181.000000 295.8000
137 1560.0 122.692949 52.253015 19.2000 81.300000 117.70000 161.600000 334.7000
138 1553.0 57.603025 12.345358 19.8000 50.900100 55.90010 62.900100 141.7998
139 1553.0 416.766964 263.300614 0.0000 243.786000 339.56100 502.205900 1770.6909
140 1553.0 26.077904 506.922106 0.0319 0.131700 0.23580 0.439100 9998.8944
141 1553.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
142 1553.0 6.641565 3.552254 1.7400 5.110000 6.26000 7.500000 103.3900
143 1558.0 0.004169 0.001282 0.0000 0.003300 0.00390 0.004900 0.0121
144 1565.0 0.120008 0.061343 0.0324 0.083900 0.10750 0.132700 0.6253
145 1565.0 0.063621 0.026541 0.0214 0.048000 0.05860 0.071800 0.2507
146 1565.0 0.055010 0.021844 0.0227 0.042300 0.05000 0.061500 0.2479
147 1565.0 0.017411 0.027123 0.0043 0.010000 0.01590 0.021300 0.9783
148 1565.0 8.471308 18.740631 1.4208 6.359900 7.91730 9.585300 742.9421
149 1564.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
150 1564.0 6.814268 3.241843 1.3370 4.459250 5.95100 8.275000 22.3180
151 1564.0 14.047403 31.002541 2.0200 8.089750 10.99350 14.347250 536.5640
152 1564.0 1.196733 23.364063 0.1544 0.373750 0.46870 0.679925 924.3780
153 1564.0 0.011926 0.009346 0.0036 0.007275 0.01110 0.014900 0.2389
154 1564.0 7.697971 5.239219 1.2438 5.926950 7.51270 9.054675 191.5478
155 1557.0 0.507171 1.122427 0.1400 0.240000 0.32000 0.450000 12.7100
156 1567.0 0.058089 0.079174 0.0111 0.036250 0.04870 0.066700 2.2016
159 1565.0 882.680511 983.043021 0.0000 411.000000 623.00000 966.000000 7791.0000
160 1565.0 555.346326 574.808588 0.0000 295.000000 438.00000 625.000000 4170.0000
161 1565.0 4066.850479 4239.245058 0.0000 1321.000000 2614.00000 5034.000000 37943.0000
162 1565.0 4797.154633 6553.569317 0.0000 451.000000 1784.00000 6384.000000 36871.0000
163 1565.0 0.140204 0.121989 0.0000 0.091000 0.12000 0.154000 0.9570
164 1565.0 0.127942 0.242534 0.0000 0.068000 0.08900 0.116000 1.8170
165 1565.0 0.252026 0.407329 0.0000 0.132000 0.18400 0.255000 3.2860
166 1565.0 2.788882 1.119756 0.8000 2.100000 2.60000 3.200000 21.1000
167 1565.0 1.235783 0.632767 0.3000 0.900000 1.20000 1.500000 16.3000
168 1565.0 0.124397 0.047639 0.0330 0.090000 0.11900 0.151000 0.7250
169 1565.0 0.400454 0.197918 0.0460 0.230000 0.41200 0.536000 1.1430
170 1566.0 0.684330 0.157468 0.2979 0.575600 0.68600 0.797300 1.1530
171 1566.0 0.120064 0.060785 0.0089 0.079800 0.11250 0.140300 0.4940
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422 1564.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
423 1564.0 77.660446 32.596933 23.0200 55.976675 69.90545 92.911500 424.2152
424 1564.0 3.315469 6.325365 0.4866 1.965250 2.66710 3.470975 103.1809
425 1564.0 6.796312 23.257716 1.4666 3.766200 4.76440 6.883500 898.6085
426 1564.0 1.233858 0.995620 0.3632 0.743425 1.13530 1.539500 24.9904
427 1564.0 4.058501 3.042144 0.6637 3.113225 3.94145 4.768650 113.2230
428 1557.0 4.220747 10.632730 1.1198 1.935500 2.53410 3.609000 118.7533
429 1567.0 4.171844 6.435390 0.7837 2.571400 3.45380 4.755800 186.6164
430 1565.0 18.421600 36.060084 0.0000 6.999700 11.10560 17.423100 400.0000
431 1565.0 22.358305 36.395408 0.0000 11.059000 16.38100 21.765200 400.0000
432 1565.0 99.367633 126.188715 0.0000 31.032400 57.96930 120.172900 994.2857
433 1565.0 205.519304 225.778870 0.0000 10.027100 151.11560 305.026300 995.7447
434 1565.0 14.733945 34.108854 0.0000 7.550700 10.19770 12.754200 400.0000
435 1565.0 9.370666 34.369789 0.0000 3.494400 4.55110 5.822800 400.0000
436 1565.0 7.513266 34.557804 0.0000 1.950900 2.76430 3.822200 400.0000
437 1565.0 4.016785 1.611274 1.1568 3.070700 3.78090 4.678600 32.2740
438 1565.0 54.701052 34.108051 0.0000 36.290300 49.09090 66.666700 851.6129
439 1565.0 70.643942 38.376178 14.1206 48.173800 65.43780 84.973400 657.7621
440 1565.0 11.526617 6.169471 1.0973 5.414100 12.08590 15.796400 33.0580
441 1566.0 0.802081 0.184213 0.3512 0.679600 0.80760 0.927600 1.2771
442 1566.0 1.345259 0.659195 0.0974 0.907650 1.26455 1.577825 5.1317
443 1566.0 0.633941 0.143552 0.2169 0.550500 0.64350 0.733425 1.0851
444 1566.0 0.895043 0.155522 0.3336 0.804800 0.90270 0.988800 1.3511
445 1566.0 0.647090 0.141252 0.3086 0.555800 0.65110 0.748400 1.1087
446 1566.0 1.175003 0.176158 0.6968 1.046800 1.16380 1.272300 1.7639
447 1566.0 0.281895 0.086461 0.0846 0.226100 0.27970 0.338825 0.5085
448 1566.0 0.332270 0.236275 0.0399 0.187700 0.25120 0.351100 1.4754
449 1543.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
450 1543.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
451 1566.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
452 1566.0 5.346816 0.919196 2.6709 4.764200 5.27145 5.913000 13.9776
453 1566.0 5.460971 2.250804 0.9037 3.747875 5.22710 6.902475 34.4902
454 1566.0 7.883742 3.059660 2.3294 5.806525 7.42490 9.576775 42.0703
455 1566.0 3.636633 0.938372 0.6948 2.899675 3.72450 4.341925 10.1840
456 1566.0 12.325685 8.125876 3.0489 8.816575 11.35090 14.387900 232.1258
457 1566.0 5.263666 4.537737 1.4428 3.827525 4.79335 6.089450 164.1093
458 1566.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
459 1566.0 2.838380 1.345576 0.9910 2.291175 2.83035 3.309225 47.7772
460 1566.0 29.197414 13.335189 7.9534 20.221850 26.16785 35.278800 149.3851
461 1566.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
462 1563.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
463 1563.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
464 1563.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
465 1563.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
466 1563.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
467 1563.0 6.252091 8.673724 1.7163 4.697500 5.64500 6.386900 109.0074
468 1560.0 224.173047 230.766915 0.0000 38.472775 150.34010 335.922400 999.8770
469 1561.0 5.662293 3.151685 2.6009 4.847200 5.47240 6.005700 77.8007
470 1561.0 5.367752 4.983367 0.8325 2.823300 4.06110 7.006800 87.1347
471 1561.0 9.638797 10.174117 2.4026 5.807300 7.39600 9.720200 212.6557
472 1560.0 137.888406 47.698041 11.4997 105.525150 138.25515 168.410125 492.7718
473 1560.0 39.426847 22.457104 0.0000 24.900800 34.24675 47.727850 358.9504
474 1560.0 37.637050 24.822918 0.0000 23.156500 32.82005 45.169475 415.4355
475 1561.0 4.262573 2.611174 1.1011 3.494500 4.27620 4.741800 79.1162
476 1561.0 20.132155 14.939590 0.0000 11.577100 15.97380 23.737200 274.8871
477 1561.0 6.257921 10.185026 1.6872 4.105400 5.24220 6.703800 289.8264
478 1561.0 0.128123 5.062075 0.0000 0.000000 0.00000 0.000000 200.0000
479 1561.0 3.283394 2.638608 0.6459 2.627700 3.18450 3.625300 63.3336
480 1561.0 75.538131 35.752493 8.8406 52.894500 70.43450 93.119600 221.9747
481 1561.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
482 1543.0 318.418448 281.011323 0.0000 0.000000 293.51850 514.585900 999.4135
483 1543.0 206.564196 192.864413 0.0000 81.316150 148.31750 262.865250 989.4737
484 1543.0 215.288948 213.126638 0.0000 76.455400 138.77550 294.667050 996.8586
485 1543.0 201.111728 218.690015 0.0000 50.383550 112.95340 288.893450 994.0000
486 1543.0 302.506186 287.364070 0.0000 0.000000 249.92700 501.607450 999.4911
487 1543.0 239.455326 263.837645 0.0000 55.555150 112.27550 397.506100 995.7447
488 1543.0 352.616477 252.043751 0.0000 139.914350 348.52940 510.647150 997.5186
489 1543.0 272.169707 228.046702 0.0000 112.859250 219.48720 377.144200 994.0035
490 1566.0 51.354045 18.048612 13.7225 38.391100 48.55745 61.494725 142.8436
491 1555.0 2.442673 1.224283 0.5558 1.747100 2.25080 2.839800 12.7698
493 1567.0 2.530046 0.973948 0.8330 1.663750 2.52910 3.199100 9.4024
494 1567.0 0.956442 6.615200 0.0342 0.139000 0.23250 0.563000 127.5728
495 1567.0 6.807826 3.260019 1.7720 5.274600 6.60790 7.897200 107.6926
496 1516.0 29.865896 24.621586 4.8135 16.342300 22.03910 32.438475 219.6436
497 1516.0 11.821030 4.956647 1.9496 8.150350 10.90655 14.469050 40.2818
498 1561.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
499 1565.0 263.195864 324.771342 0.0000 0.000000 0.00000 536.204600 1000.0000
500 1565.0 240.981377 323.003410 0.0000 0.000000 0.00000 505.401000 999.2337
501 1561.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
502 1561.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
503 1561.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
504 1561.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
505 1561.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
506 1561.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
507 1561.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
508 1561.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
509 1561.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
510 1565.0 55.763508 37.691736 0.0000 35.322200 46.98610 64.248700 451.4851
511 1565.0 275.979457 329.664680 0.0000 0.000000 0.00000 555.294100 1000.0000
512 1561.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
513 1561.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
514 1561.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
515 1561.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
519 852.0 11.728440 15.814420 0.0000 4.160300 5.83295 10.971850 184.3488
520 1567.0 2.695999 5.702366 0.3121 1.552150 2.22100 2.903700 111.7365
521 1567.0 11.610080 103.122996 0.0000 0.000000 0.00000 0.000000 1000.0000
522 1567.0 14.728866 7.104435 2.6811 10.182800 13.74260 17.808950 137.9838
523 1567.0 0.453896 4.147581 0.0258 0.073050 0.10000 0.133200 111.3330
524 1567.0 5.687782 20.663414 1.3104 3.769650 4.87710 6.450650 818.0005
525 1543.0 5.560397 3.920370 1.5400 4.101500 5.13420 6.329500 80.0406
526 1567.0 1.443457 0.958428 0.1705 0.484200 1.55010 2.211650 8.2037
527 1567.0 6.395717 1.888698 2.1700 4.895450 6.41080 7.594250 14.4479
528 1558.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
529 1558.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
530 1558.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
531 1558.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
532 1558.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
533 1558.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
534 1558.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
535 1558.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
536 1558.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
537 1558.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
538 1558.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
539 1559.0 3.034235 1.252913 0.8516 1.889900 3.05480 3.947000 6.5803
540 1559.0 1.942828 0.731928 0.6144 1.385300 1.78550 2.458350 4.0825
541 1559.0 9.611628 2.896376 3.2761 7.495750 9.45930 11.238400 25.7792
542 1565.0 0.111208 0.002737 0.1053 0.109600 0.10960 0.113400 0.1184
543 1565.0 0.008471 0.001534 0.0051 0.007800 0.00780 0.009000 0.0240
544 1565.0 0.002509 0.000296 0.0016 0.002400 0.00260 0.002600 0.0047
545 1565.0 7.611403 1.315544 4.4294 7.116000 7.11600 8.020700 21.0443
546 1307.0 1.039630 0.389066 0.4444 0.797500 0.91110 1.285550 3.9786
547 1307.0 403.546477 5.063887 372.8220 400.694000 403.12200 407.431000 421.7020
548 1307.0 75.679871 3.390523 71.0380 73.254000 74.08400 78.397000 83.7200
549 1307.0 0.663256 0.673346 0.0446 0.226250 0.47100 0.850350 7.0656
550 1307.0 17.013313 4.966954 6.1100 14.530000 16.34000 19.035000 131.6800
551 1307.0 1.230712 1.361117 0.1200 0.870000 1.15000 1.370000 39.3300
552 1307.0 0.276688 0.276231 0.0187 0.094900 0.19790 0.358450 2.7182
553 1307.0 7.703874 2.192647 2.7860 6.738100 7.42790 8.637150 56.9303
554 1307.0 0.503657 0.598852 0.0520 0.343800 0.47890 0.562350 17.4781
555 1307.0 57.746537 35.207552 4.8269 27.017600 54.44170 74.628700 303.5500
556 1307.0 4.216905 1.280008 1.4967 3.625100 4.06710 4.702700 35.3198
557 1307.0 1.623070 1.870433 0.1646 1.182900 1.52980 1.815600 54.2917
558 1566.0 0.995009 0.083860 0.8919 0.955200 0.97270 1.000800 1.5121
559 1566.0 0.325708 0.201392 0.0699 0.149825 0.29090 0.443600 1.0737
560 1566.0 0.072443 0.051578 0.0177 0.036200 0.05920 0.089000 0.4457
561 1566.0 32.284956 19.026081 7.2369 15.762450 29.73115 44.113400 101.1146
562 1294.0 262.729683 7.630585 242.2860 259.972500 264.27200 265.707000 311.4040
563 1294.0 0.679641 0.121758 0.3049 0.567100 0.65100 0.768875 1.2988
564 1294.0 6.444985 2.633583 0.9700 4.980000 5.16000 7.800000 32.5800
565 1294.0 0.145610 0.081122 0.0224 0.087700 0.11955 0.186150 0.6892
566 1294.0 2.610870 1.032761 0.4122 2.090200 2.15045 3.098725 14.0141
567 1294.0 0.060086 0.032761 0.0091 0.038200 0.04865 0.075275 0.2932
568 1294.0 2.452417 0.996644 0.3706 1.884400 1.99970 2.970850 12.7462
569 1294.0 21.117674 10.213294 3.2504 15.466200 16.98835 24.772175 84.8024
570 1567.0 530.523623 17.499736 317.1964 530.702700 532.39820 534.356400 589.5082
571 1567.0 2.101836 0.275112 0.9802 1.982900 2.11860 2.290650 2.7395
572 1567.0 28.450165 86.304681 3.5400 7.500000 8.65000 10.130000 454.5600
573 1567.0 0.345636 0.248478 0.0667 0.242250 0.29340 0.366900 2.1967
574 1567.0 9.162315 26.920150 1.0395 2.567850 2.97580 3.492500 170.0204
575 1567.0 0.104729 0.067791 0.0230 0.075100 0.08950 0.112150 0.5502
576 1567.0 5.563747 16.921369 0.6636 1.408450 1.62450 1.902000 90.4235
577 1567.0 16.642363 12.485267 4.5820 11.501550 13.81790 17.080900 96.9601
578 618.0 0.021615 0.011730 -0.0169 0.013800 0.02040 0.027700 0.1028
579 618.0 0.016829 0.009640 0.0032 0.010600 0.01480 0.020000 0.0799
580 618.0 0.005396 0.003116 0.0010 0.003400 0.00470 0.006475 0.0286
581 618.0 97.934373 87.520966 0.0000 46.184900 72.28890 116.539150 737.3048
582 1566.0 0.500096 0.003404 0.4778 0.497900 0.50020 0.502375 0.5098
583 1566.0 0.015318 0.017180 0.0060 0.011600 0.01380 0.016500 0.4766
584 1566.0 0.003847 0.003720 0.0017 0.003100 0.00360 0.004100 0.1045
585 1566.0 3.067826 3.578033 1.1975 2.306500 2.75765 3.295175 99.3032
586 1566.0 0.021458 0.012358 -0.0169 0.013425 0.02050 0.027600 0.1028
587 1566.0 0.016475 0.008808 0.0032 0.010600 0.01480 0.020300 0.0799
588 1566.0 0.005283 0.002867 0.0010 0.003300 0.00460 0.006400 0.0286
589 1566.0 99.670066 93.891919 0.0000 44.368600 71.90050 114.749700 737.3048
Pass/Fail 1567.0 -0.867262 0.498010 -1.0000 -1.000000 -1.00000 -1.000000 1.0000
In [11]:
# We can see that manu columns have same values across all rows, such columns wont support in creating our model, 
# hence such columns can be dropped too
counter  = 0
for columns in Data.columns:
    if Data[columns].min() == Data[columns].median() and Data[columns].max() == Data[columns].median():
        counter = counter + 1
        print( columns , 'Column has single value ', Data[columns].median(), ', hence can be dropped')
        del Data[columns]
        

print('New shape of the data set after deleting above', counter ,' columns is', Data.shape)
5 Column has single value  100.0 , hence can be dropped
13 Column has single value  0.0 , hence can be dropped
42 Column has single value  70.0 , hence can be dropped
49 Column has single value  1.0 , hence can be dropped
52 Column has single value  0.0 , hence can be dropped
69 Column has single value  1.0 , hence can be dropped
97 Column has single value  0.0 , hence can be dropped
141 Column has single value  0.0 , hence can be dropped
149 Column has single value  0.0 , hence can be dropped
178 Column has single value  0.0 , hence can be dropped
179 Column has single value  0.0 , hence can be dropped
186 Column has single value  0.0 , hence can be dropped
189 Column has single value  0.0 , hence can be dropped
190 Column has single value  0.0 , hence can be dropped
191 Column has single value  0.0 , hence can be dropped
192 Column has single value  0.0 , hence can be dropped
193 Column has single value  0.0 , hence can be dropped
194 Column has single value  0.0 , hence can be dropped
226 Column has single value  0.0 , hence can be dropped
229 Column has single value  0.0 , hence can be dropped
230 Column has single value  0.0 , hence can be dropped
231 Column has single value  0.0 , hence can be dropped
232 Column has single value  0.0 , hence can be dropped
233 Column has single value  0.0 , hence can be dropped
234 Column has single value  0.0 , hence can be dropped
235 Column has single value  0.0 , hence can be dropped
236 Column has single value  0.0 , hence can be dropped
237 Column has single value  0.0 , hence can be dropped
240 Column has single value  0.0 , hence can be dropped
241 Column has single value  0.0 , hence can be dropped
242 Column has single value  0.0 , hence can be dropped
243 Column has single value  0.0 , hence can be dropped
256 Column has single value  0.0 , hence can be dropped
257 Column has single value  0.0 , hence can be dropped
258 Column has single value  0.0 , hence can be dropped
259 Column has single value  0.0 , hence can be dropped
260 Column has single value  0.0 , hence can be dropped
261 Column has single value  0.0 , hence can be dropped
262 Column has single value  0.0 , hence can be dropped
263 Column has single value  0.0 , hence can be dropped
264 Column has single value  0.0 , hence can be dropped
265 Column has single value  0.0 , hence can be dropped
266 Column has single value  0.0 , hence can be dropped
276 Column has single value  0.0 , hence can be dropped
284 Column has single value  0.0 , hence can be dropped
313 Column has single value  0.0 , hence can be dropped
314 Column has single value  0.0 , hence can be dropped
315 Column has single value  0.0 , hence can be dropped
322 Column has single value  0.0 , hence can be dropped
325 Column has single value  0.0 , hence can be dropped
326 Column has single value  0.0 , hence can be dropped
327 Column has single value  0.0 , hence can be dropped
328 Column has single value  0.0 , hence can be dropped
329 Column has single value  0.0 , hence can be dropped
330 Column has single value  0.0 , hence can be dropped
364 Column has single value  0.0 , hence can be dropped
369 Column has single value  0.0 , hence can be dropped
370 Column has single value  0.0 , hence can be dropped
371 Column has single value  0.0 , hence can be dropped
372 Column has single value  0.0 , hence can be dropped
373 Column has single value  0.0 , hence can be dropped
374 Column has single value  0.0 , hence can be dropped
375 Column has single value  0.0 , hence can be dropped
378 Column has single value  0.0 , hence can be dropped
379 Column has single value  0.0 , hence can be dropped
380 Column has single value  0.0 , hence can be dropped
381 Column has single value  0.0 , hence can be dropped
394 Column has single value  0.0 , hence can be dropped
395 Column has single value  0.0 , hence can be dropped
396 Column has single value  0.0 , hence can be dropped
397 Column has single value  0.0 , hence can be dropped
398 Column has single value  0.0 , hence can be dropped
399 Column has single value  0.0 , hence can be dropped
400 Column has single value  0.0 , hence can be dropped
401 Column has single value  0.0 , hence can be dropped
402 Column has single value  0.0 , hence can be dropped
403 Column has single value  0.0 , hence can be dropped
404 Column has single value  0.0 , hence can be dropped
414 Column has single value  0.0 , hence can be dropped
422 Column has single value  0.0 , hence can be dropped
449 Column has single value  0.0 , hence can be dropped
450 Column has single value  0.0 , hence can be dropped
451 Column has single value  0.0 , hence can be dropped
458 Column has single value  0.0 , hence can be dropped
461 Column has single value  0.0 , hence can be dropped
462 Column has single value  0.0 , hence can be dropped
463 Column has single value  0.0 , hence can be dropped
464 Column has single value  0.0 , hence can be dropped
465 Column has single value  0.0 , hence can be dropped
466 Column has single value  0.0 , hence can be dropped
481 Column has single value  0.0 , hence can be dropped
498 Column has single value  0.0 , hence can be dropped
501 Column has single value  0.0 , hence can be dropped
502 Column has single value  0.0 , hence can be dropped
503 Column has single value  0.0 , hence can be dropped
504 Column has single value  0.0 , hence can be dropped
505 Column has single value  0.0 , hence can be dropped
506 Column has single value  0.0 , hence can be dropped
507 Column has single value  0.0 , hence can be dropped
508 Column has single value  0.0 , hence can be dropped
509 Column has single value  0.0 , hence can be dropped
512 Column has single value  0.0 , hence can be dropped
513 Column has single value  0.0 , hence can be dropped
514 Column has single value  0.0 , hence can be dropped
515 Column has single value  0.0 , hence can be dropped
528 Column has single value  0.0 , hence can be dropped
529 Column has single value  0.0 , hence can be dropped
530 Column has single value  0.0 , hence can be dropped
531 Column has single value  0.0 , hence can be dropped
532 Column has single value  0.0 , hence can be dropped
533 Column has single value  0.0 , hence can be dropped
534 Column has single value  0.0 , hence can be dropped
535 Column has single value  0.0 , hence can be dropped
536 Column has single value  0.0 , hence can be dropped
537 Column has single value  0.0 , hence can be dropped
538 Column has single value  0.0 , hence can be dropped
New shape of the data set after deleting above 116  columns is (1567, 455)
In [12]:
#Lets see if we have features with very less variance, if we have any then we can drop those features too, 
# since column haveing very low variance won't be helpfull in building our model 
Data.var(axis = 0, skipna = True)
Out[12]:
0            5.420167e+03
1            6.465399e+03
2            8.710261e+02
3            1.950915e+05
4            3.175947e+03
6            3.890284e+01
7            8.030522e-05
8            5.460702e-03
9            2.284992e-04
10           8.652916e-05
11           1.550536e-04
12           1.060984e+01
14           7.820947e+00
15           2.965661e+02
16           5.778575e+00
17           1.455018e-04
18           7.734187e+00
19           4.750885e-02
20           2.801249e-04
21           3.929060e+05
22           8.731938e+04
23           1.904848e+06
24           8.425610e+06
25           3.154193e-02
26           3.590837e-02
27           1.548156e+00
28           1.197977e+01
29           1.670310e-01
30           1.085303e-03
31           2.865695e-01
32           4.106902e+00
33           1.807563e+00
34           1.398586e+00
35           6.629330e+00
36           1.398587e+00
37           9.250163e-02
38           1.995906e-01
39           3.266047e+00
40           5.790252e+02
41           5.571606e+00
43           3.887156e+01
44           3.063816e-02
45           6.161069e+01
46           1.481166e+02
47           3.596216e-02
48           2.046885e+01
50           7.471848e+01
51           3.711869e+03
53           3.019461e-03
54           3.549857e-03
55           6.630273e+02
56           4.634017e-05
57           1.743858e-05
58           7.241121e-03
59           9.086321e+01
60           3.633544e+01
61           7.555730e-02
62           7.446001e+01
63           5.069245e+01
64           2.477518e+01
65           5.071865e+01
66           1.350960e+02
67           9.455766e+04
68           1.797841e+01
70           9.099615e+01
71           1.001843e+03
72           3.381362e+02
73           3.108129e+02
74           1.127625e-02
75           4.969407e-04
76           1.102458e-03
77           9.839660e-04
78           2.291757e-03
79           5.326701e-04
80           2.423201e-03
81           2.897187e-04
82           1.301356e-03
83           2.665155e-01
84           2.551565e-05
86           1.393668e-03
87           1.650670e-04
88           2.866238e+03
89           2.742917e-03
90           1.570645e+05
91           7.688300e-03
92           1.043952e-05
93           9.059099e-06
94           3.032293e-08
95           1.090102e-08
96           4.821456e-02
98           1.824228e-01
99           3.936357e-03
100          1.264063e-07
101          4.873603e-08
102          3.964927e-03
103          9.391460e-06
104          7.237052e-07
105          1.025491e-05
106          8.927623e-06
107          7.651836e-03
108          7.526910e-03
112          2.395073e-03
113          1.472066e-04
114          2.782538e-06
115          2.396029e+03
116          9.018359e-05
117          4.205749e+01
118          6.563458e-05
119          8.007676e-05
120          1.545158e-02
121          9.923691e-03
122          8.174338e-01
123          1.173213e-02
124          1.302878e-02
125          7.871093e-02
126          6.424745e-02
127          1.833556e-02
128          6.978819e-02
129          1.489568e+00
130          6.811409e-03
131          5.065094e-06
132          2.828198e-03
133          4.274154e+01
134          8.942947e+00
135          3.311384e+03
136          2.906266e+03
137          2.730378e+03
138          1.524079e+02
139          6.932721e+04
140          2.569700e+05
142          1.261851e+01
143          1.643035e-06
144          3.762937e-03
145          7.044026e-04
146          4.771816e-04
147          7.356522e-04
148          3.512113e+02
150          1.050954e+01
151          9.611576e+02
152          5.458794e+02
153          8.734168e-05
154          2.744942e+01
155          1.259842e+00
156          6.268600e-03
159          9.663736e+05
160          3.304049e+05
161          1.797120e+07
162          4.294927e+07
163          1.488131e-02
164          5.882256e-02
165          1.659172e-01
166          1.253853e+00
167          4.003940e-01
168          2.269439e-03
169          3.917138e-02
170          2.479616e-02
171          3.694800e-03
172          5.075566e-03
173          9.164992e-03
174          5.076119e-03
175          1.353084e-02
176          5.612675e-03
177          8.003409e-02
180          1.096691e+01
181          5.035615e-02
182          1.733932e+01
183          4.673228e+01
184          1.214354e-02
185          5.167770e+01
187          7.413058e+01
188          4.714056e+02
195          1.561727e-01
196          2.471475e+02
197          1.113481e+02
198          2.891269e-01
199          2.704563e+02
200          7.552859e+01
201          2.605587e+01
202          2.138293e+02
203          3.049144e+02
204          3.193394e+05
205          1.331966e+02
206          2.562460e-03
207          3.061645e+02
208          7.877645e+02
209          1.364396e+00
210          1.769425e-03
211          6.252572e-04
212          9.971476e-04
213          2.812135e-03
214          3.187243e-03
215          9.264001e-04
216          6.637996e-04
217          2.142159e-03
218          1.369921e+00
219          2.709667e-06
221          5.431336e-04
222          3.128922e-03
223          3.042185e+03
224          5.071041e-03
225          1.876363e+05
227          1.156854e-04
228          1.154524e-04
238          2.883027e-06
239          2.077649e-06
247          4.472961e-03
248          2.424092e-03
249          2.487177e-04
250          2.980862e+03
251          1.404188e-03
252          4.141535e+03
253          5.028854e-04
254          8.339595e-05
255          1.448031e-02
267          8.790437e-04
268          5.394028e+01
269          1.327862e+00
270          7.059382e+01
271          3.192096e+02
272          3.146194e+02
273          1.467244e+01
274          7.328693e+03
275          2.854390e+04
277          1.431462e+00
278          1.156231e-07
279          4.116502e-04
280          4.202943e-05
281          3.075236e-05
282          7.310877e-05
283          3.439029e+01
285          9.272202e-01
286          9.533236e+01
287          5.455806e+01
288          8.620656e-06
289          2.614667e+00
290          7.343397e-02
291          6.527423e-04
294          2.275768e+05
295          8.038966e+04
296          3.901065e+06
297          1.041304e+07
298          4.124834e-03
299          1.711528e-02
300          4.802548e-02
301          1.102118e-01
302          3.901178e-02
303          2.105579e-04
304          4.207780e-03
305          3.293324e-03
306          6.451579e-04
307          7.544716e-04
308          1.128504e-03
309          7.546067e-04
310          1.888758e-03
311          8.292196e-04
312          1.376298e-02
316          1.037605e+00
317          5.240654e-03
318          1.478486e+00
319          4.748297e+00
320          1.016640e-03
321          4.481666e+00
323          6.344652e+00
324          4.376947e+01
331          4.022668e-03
332          3.186857e+01
333          1.158345e+01
334          2.988838e-02
335          3.342642e+01
336          5.709511e+01
337          2.888079e+00
338          3.186627e+01
339          3.690200e+01
340          6.850702e+04
341          1.345350e+01
342          1.281152e-04
343          2.885650e+01
344          7.912496e+01
345          3.067040e+02
346          2.916409e+02
347          1.240352e-01
348          1.407185e-04
349          1.124280e-04
350          2.052244e-04
351          6.033369e-04
352          1.731107e-04
353          2.402275e-04
354          1.707700e-04
355          4.975885e-04
356          1.497052e-01
357          2.509253e-07
359          5.092760e-05
360          4.001028e-04
361          2.909175e+02
362          4.684651e-04
363          1.926598e+04
365          7.054390e-06
366          5.676064e-06
367          7.285036e-06
368          4.438111e-06
376          2.855300e-07
377          2.176596e-07
385          2.063713e-04
386          2.398823e-04
387          2.489346e-05
388          2.967696e+02
389          1.396180e-04
390          4.131632e+02
391          4.539671e-05
392          8.735296e-06
393          1.475212e-03
405          1.150958e-04
406          8.006542e+00
407          1.330142e-01
408          6.646691e+00
409          3.157172e+00
410          4.507035e+00
411          3.041238e-01
412          3.390615e+02
413          2.238091e+03
415          1.566870e+01
416          1.072122e+00
417          1.643909e+01
418          8.277387e+04
419          1.059167e+05
420          9.349482e+00
421          4.780139e+01
423          1.062560e+03
424          4.001024e+01
425          5.409213e+02
426          9.912593e-01
427          9.254643e+00
428          1.130549e+02
429          4.141425e+01
430          1.300330e+03
431          1.324626e+03
432          1.592359e+04
433          5.097610e+04
434          1.163414e+03
435          1.181282e+03
436          1.194242e+03
437          2.596203e+00
438          1.163359e+03
439          1.472731e+03
440          3.806237e+01
441          3.393432e-02
442          4.345375e-01
443          2.060719e-02
444          2.418700e-02
445          1.995218e-02
446          3.103171e-02
447          7.475464e-03
448          5.582603e-02
452          8.449220e-01
453          5.066121e+00
454          9.361522e+00
455          8.805422e-01
456          6.602986e+01
457          2.059105e+01
459          1.810576e+00
460          1.778273e+02
467          7.523348e+01
468          5.325337e+04
469          9.933116e+00
470          2.483394e+01
471          1.035127e+02
472          2.275103e+03
473          5.043215e+02
474          6.161773e+02
475          6.818230e+00
476          2.231913e+02
477          1.037348e+02
478          2.562460e+01
479          6.962254e+00
480          1.278241e+03
482          7.896736e+04
483          3.719668e+04
484          4.542296e+04
485          4.782532e+04
486          8.257811e+04
487          6.961030e+04
488          6.352605e+04
489          5.200530e+04
490          3.257524e+02
491          1.498868e+00
493          9.485753e-01
494          4.376087e+01
495          1.062773e+01
496          6.062225e+02
497          2.456835e+01
499          1.054764e+05
500          1.043312e+05
510          1.420667e+03
511          1.086788e+05
519          2.500959e+02
520          3.251698e+01
521          1.063435e+04
522          5.047300e+01
523          1.720243e+01
524          4.269767e+02
525          1.536930e+01
526          9.185833e-01
527          3.567179e+00
539          1.569791e+00
540          5.357191e-01
541          8.388993e+00
542          7.489852e-06
543          2.351759e-06
544          8.733216e-08
545          1.730657e+00
546          1.513722e-01
547          2.564295e+01
548          1.149565e+01
549          4.533945e-01
550          2.467063e+01
551          1.852640e+00
552          7.630337e-02
553          4.807702e+00
554          3.586237e-01
555          1.239572e+03
556          1.638422e+00
557          3.498521e+00
558          7.032422e-03
559          4.055869e-02
560          2.660272e-03
561          3.619918e+02
562          5.822583e+01
563          1.482495e-02
564          6.935761e+00
565          6.580836e-03
566          1.066596e+00
567          1.073280e-03
568          9.932996e-01
569          1.043114e+02
570          3.062408e+02
571          7.568653e-02
572          7.448498e+03
573          6.174138e-02
574          7.246945e+02
575          4.595636e-03
576          2.863327e+02
577          1.558819e+02
578          1.376002e-04
579          9.293216e-05
580          9.709368e-06
581          7.659920e+03
582          1.158943e-05
583          2.951497e-04
584          1.384171e-05
585          1.280232e+01
586          1.527245e-04
587          7.757268e-05
588          8.220099e-06
589          8.815693e+03
Pass/Fail    2.480144e-01
dtype: float64
In [13]:
#We can see that we have many features with very low variance,
#lets get rid of such features which has variance less than 10%
counter  = 0
for columns in Data.columns[:454]: # leaving the last column
    if Data[columns].var() <=10:
        counter = counter + 1
        print( columns , 'Column has variance of ', Data[columns].var(), 'which is very low, hence can be dropped')
        del Data[columns]
        

print('New shape of the data set after deleting above', counter ,' columns is', Data.shape)
7 Column has variance of  8.030522137796683e-05 which is very low, hence can be dropped
8 Column has variance of  0.0054607018028647765 which is very low, hence can be dropped
9 Column has variance of  0.00022849918565487037 which is very low, hence can be dropped
10 Column has variance of  8.652915872302494e-05 which is very low, hence can be dropped
11 Column has variance of  0.00015505359361185774 which is very low, hence can be dropped
14 Column has variance of  7.820946786353919 which is very low, hence can be dropped
16 Column has variance of  5.778574796383628 which is very low, hence can be dropped
17 Column has variance of  0.0001455017992932797 which is very low, hence can be dropped
18 Column has variance of  7.734187455719755 which is very low, hence can be dropped
19 Column has variance of  0.04750885460969863 which is very low, hence can be dropped
20 Column has variance of  0.00028012491013976854 which is very low, hence can be dropped
25 Column has variance of  0.03154192896995499 which is very low, hence can be dropped
26 Column has variance of  0.03590837324042573 which is very low, hence can be dropped
27 Column has variance of  1.5481562508658315 which is very low, hence can be dropped
29 Column has variance of  0.1670309511443572 which is very low, hence can be dropped
30 Column has variance of  0.0010853033811722226 which is very low, hence can be dropped
31 Column has variance of  0.2865694657314093 which is very low, hence can be dropped
32 Column has variance of  4.10690168344204 which is very low, hence can be dropped
33 Column has variance of  1.8075629222614 which is very low, hence can be dropped
34 Column has variance of  1.3985857497574437 which is very low, hence can be dropped
35 Column has variance of  6.629330325793535 which is very low, hence can be dropped
36 Column has variance of  1.3985874294421847 which is very low, hence can be dropped
37 Column has variance of  0.09250162542205558 which is very low, hence can be dropped
38 Column has variance of  0.1995905503449948 which is very low, hence can be dropped
39 Column has variance of  3.266047230814435 which is very low, hence can be dropped
41 Column has variance of  5.571606134393028 which is very low, hence can be dropped
44 Column has variance of  0.030638159733130922 which is very low, hence can be dropped
47 Column has variance of  0.03596215621214383 which is very low, hence can be dropped
53 Column has variance of  0.003019460758267987 which is very low, hence can be dropped
54 Column has variance of  0.0035498565580653093 which is very low, hence can be dropped
56 Column has variance of  4.634017080321758e-05 which is very low, hence can be dropped
57 Column has variance of  1.743857661527828e-05 which is very low, hence can be dropped
58 Column has variance of  0.007241120885653585 which is very low, hence can be dropped
61 Column has variance of  0.07555730046428144 which is very low, hence can be dropped
74 Column has variance of  0.011276246156309962 which is very low, hence can be dropped
75 Column has variance of  0.0004969407105601385 which is very low, hence can be dropped
76 Column has variance of  0.0011024577626164926 which is very low, hence can be dropped
77 Column has variance of  0.0009839660465110422 which is very low, hence can be dropped
78 Column has variance of  0.0022917572584526735 which is very low, hence can be dropped
79 Column has variance of  0.0005326701365019892 which is very low, hence can be dropped
80 Column has variance of  0.002423200925908655 which is very low, hence can be dropped
81 Column has variance of  0.00028971867724454105 which is very low, hence can be dropped
82 Column has variance of  0.001301355798026818 which is very low, hence can be dropped
83 Column has variance of  0.2665154925133077 which is very low, hence can be dropped
84 Column has variance of  2.5515645242854266e-05 which is very low, hence can be dropped
86 Column has variance of  0.0013936678611708101 which is very low, hence can be dropped
87 Column has variance of  0.00016506704640163736 which is very low, hence can be dropped
89 Column has variance of  0.0027429169334404328 which is very low, hence can be dropped
91 Column has variance of  0.007688300488181476 which is very low, hence can be dropped
92 Column has variance of  1.043951756371396e-05 which is very low, hence can be dropped
93 Column has variance of  9.059099482771316e-06 which is very low, hence can be dropped
94 Column has variance of  3.0322927446245835e-08 which is very low, hence can be dropped
95 Column has variance of  1.0901024983984442e-08 which is very low, hence can be dropped
96 Column has variance of  0.04821456154575472 which is very low, hence can be dropped
98 Column has variance of  0.18242276916571443 which is very low, hence can be dropped
99 Column has variance of  0.003936356967681807 which is very low, hence can be dropped
100 Column has variance of  1.2640633880319945e-07 which is very low, hence can be dropped
101 Column has variance of  4.873602555889598e-08 which is very low, hence can be dropped
102 Column has variance of  0.0039649267096042995 which is very low, hence can be dropped
103 Column has variance of  9.391459818765717e-06 which is very low, hence can be dropped
104 Column has variance of  7.237051878120312e-07 which is very low, hence can be dropped
105 Column has variance of  1.0254912194681282e-05 which is very low, hence can be dropped
106 Column has variance of  8.927622595640542e-06 which is very low, hence can be dropped
107 Column has variance of  0.007651836337760147 which is very low, hence can be dropped
108 Column has variance of  0.007526909831427886 which is very low, hence can be dropped
112 Column has variance of  0.0023950727386587455 which is very low, hence can be dropped
113 Column has variance of  0.0001472065857839001 which is very low, hence can be dropped
114 Column has variance of  2.782538181735315e-06 which is very low, hence can be dropped
116 Column has variance of  9.018359277923213e-05 which is very low, hence can be dropped
118 Column has variance of  6.563458496721313e-05 which is very low, hence can be dropped
119 Column has variance of  8.00767608750401e-05 which is very low, hence can be dropped
120 Column has variance of  0.015451581590433616 which is very low, hence can be dropped
121 Column has variance of  0.009923690888719047 which is very low, hence can be dropped
122 Column has variance of  0.8174338282026655 which is very low, hence can be dropped
123 Column has variance of  0.01173212569348089 which is very low, hence can be dropped
124 Column has variance of  0.013028782392326488 which is very low, hence can be dropped
125 Column has variance of  0.07871093279650547 which is very low, hence can be dropped
126 Column has variance of  0.0642474541777042 which is very low, hence can be dropped
127 Column has variance of  0.018335560840219728 which is very low, hence can be dropped
128 Column has variance of  0.06978818897306724 which is very low, hence can be dropped
129 Column has variance of  1.4895683782156268 which is very low, hence can be dropped
130 Column has variance of  0.00681140948330165 which is very low, hence can be dropped
131 Column has variance of  5.065094108927022e-06 which is very low, hence can be dropped
132 Column has variance of  0.002828197864427096 which is very low, hence can be dropped
134 Column has variance of  8.942947204486611 which is very low, hence can be dropped
143 Column has variance of  1.6430351479054807e-06 which is very low, hence can be dropped
144 Column has variance of  0.0037629373318026193 which is very low, hence can be dropped
145 Column has variance of  0.0007044025657975374 which is very low, hence can be dropped
146 Column has variance of  0.00047718164481994963 which is very low, hence can be dropped
147 Column has variance of  0.0007356522448624469 which is very low, hence can be dropped
153 Column has variance of  8.734167889804659e-05 which is very low, hence can be dropped
155 Column has variance of  1.2598418658186799 which is very low, hence can be dropped
156 Column has variance of  0.006268599505444745 which is very low, hence can be dropped
163 Column has variance of  0.014881313662845466 which is very low, hence can be dropped
164 Column has variance of  0.05882256318687977 which is very low, hence can be dropped
165 Column has variance of  0.16591717837444642 which is very low, hence can be dropped
166 Column has variance of  1.2538532884469245 which is very low, hence can be dropped
167 Column has variance of  0.4003939681164857 which is very low, hence can be dropped
168 Column has variance of  0.0022694389923437106 which is very low, hence can be dropped
169 Column has variance of  0.0391713822834871 which is very low, hence can be dropped
170 Column has variance of  0.024796161999506305 which is very low, hence can be dropped
171 Column has variance of  0.0036948002448026944 which is very low, hence can be dropped
172 Column has variance of  0.0050755658751994205 which is very low, hence can be dropped
173 Column has variance of  0.009164992446403014 which is very low, hence can be dropped
174 Column has variance of  0.005076118763304898 which is very low, hence can be dropped
175 Column has variance of  0.013530839840985957 which is very low, hence can be dropped
176 Column has variance of  0.005612675480183944 which is very low, hence can be dropped
177 Column has variance of  0.08003408544510127 which is very low, hence can be dropped
181 Column has variance of  0.050356146480114584 which is very low, hence can be dropped
184 Column has variance of  0.01214353542877193 which is very low, hence can be dropped
195 Column has variance of  0.15617273678118296 which is very low, hence can be dropped
198 Column has variance of  0.28912687634816603 which is very low, hence can be dropped
206 Column has variance of  0.002562459961563105 which is very low, hence can be dropped
209 Column has variance of  1.3643962203715427 which is very low, hence can be dropped
210 Column has variance of  0.0017694254949636586 which is very low, hence can be dropped
211 Column has variance of  0.0006252572111363548 which is very low, hence can be dropped
212 Column has variance of  0.0009971475888599435 which is very low, hence can be dropped
213 Column has variance of  0.002812134652760093 which is very low, hence can be dropped
214 Column has variance of  0.003187242900736602 which is very low, hence can be dropped
215 Column has variance of  0.0009264001095193327 which is very low, hence can be dropped
216 Column has variance of  0.0006637996380541214 which is very low, hence can be dropped
217 Column has variance of  0.0021421589156585996 which is very low, hence can be dropped
218 Column has variance of  1.3699206375617323 which is very low, hence can be dropped
219 Column has variance of  2.709666910824481e-06 which is very low, hence can be dropped
221 Column has variance of  0.000543133593480152 which is very low, hence can be dropped
222 Column has variance of  0.0031289219135326963 which is very low, hence can be dropped
224 Column has variance of  0.005071041370359711 which is very low, hence can be dropped
227 Column has variance of  0.00011568535685511909 which is very low, hence can be dropped
228 Column has variance of  0.00011545240637997116 which is very low, hence can be dropped
238 Column has variance of  2.8830265641469716e-06 which is very low, hence can be dropped
239 Column has variance of  2.0776490443934183e-06 which is very low, hence can be dropped
247 Column has variance of  0.004472960982150241 which is very low, hence can be dropped
248 Column has variance of  0.0024240922937240924 which is very low, hence can be dropped
249 Column has variance of  0.0002487177487222367 which is very low, hence can be dropped
251 Column has variance of  0.00140418766188983 which is very low, hence can be dropped
253 Column has variance of  0.0005028853663715393 which is very low, hence can be dropped
254 Column has variance of  8.339595473694748e-05 which is very low, hence can be dropped
255 Column has variance of  0.014480312089365502 which is very low, hence can be dropped
267 Column has variance of  0.0008790437182667847 which is very low, hence can be dropped
269 Column has variance of  1.3278623084429109 which is very low, hence can be dropped
277 Column has variance of  1.431462163837263 which is very low, hence can be dropped
278 Column has variance of  1.1562307950429757e-07 which is very low, hence can be dropped
279 Column has variance of  0.0004116502037456183 which is very low, hence can be dropped
280 Column has variance of  4.202943019046751e-05 which is very low, hence can be dropped
281 Column has variance of  3.075236236241965e-05 which is very low, hence can be dropped
282 Column has variance of  7.310877011513063e-05 which is very low, hence can be dropped
285 Column has variance of  0.9272202024925948 which is very low, hence can be dropped
288 Column has variance of  8.620655585609012e-06 which is very low, hence can be dropped
289 Column has variance of  2.614667248896111 which is very low, hence can be dropped
290 Column has variance of  0.07343396952895369 which is very low, hence can be dropped
291 Column has variance of  0.0006527422682057519 which is very low, hence can be dropped
298 Column has variance of  0.004124833624482154 which is very low, hence can be dropped
299 Column has variance of  0.01711528069619148 which is very low, hence can be dropped
300 Column has variance of  0.04802548035925769 which is very low, hence can be dropped
301 Column has variance of  0.11021184043908873 which is very low, hence can be dropped
302 Column has variance of  0.039011778068873924 which is very low, hence can be dropped
303 Column has variance of  0.00021055787276010558 which is very low, hence can be dropped
304 Column has variance of  0.004207780405799822 which is very low, hence can be dropped
305 Column has variance of  0.003293323864733424 which is very low, hence can be dropped
306 Column has variance of  0.0006451578550753018 which is very low, hence can be dropped
307 Column has variance of  0.0007544715993618364 which is very low, hence can be dropped
308 Column has variance of  0.0011285041357480682 which is very low, hence can be dropped
309 Column has variance of  0.0007546066849179246 which is very low, hence can be dropped
310 Column has variance of  0.0018887582044687665 which is very low, hence can be dropped
311 Column has variance of  0.0008292196066574446 which is very low, hence can be dropped
312 Column has variance of  0.013762984826786482 which is very low, hence can be dropped
316 Column has variance of  1.0376054107044184 which is very low, hence can be dropped
317 Column has variance of  0.005240653758583965 which is very low, hence can be dropped
318 Column has variance of  1.4784856824773227 which is very low, hence can be dropped
319 Column has variance of  4.748297235151143 which is very low, hence can be dropped
320 Column has variance of  0.0010166399821975734 which is very low, hence can be dropped
321 Column has variance of  4.481665675012632 which is very low, hence can be dropped
323 Column has variance of  6.344652353984891 which is very low, hence can be dropped
331 Column has variance of  0.004022667883023151 which is very low, hence can be dropped
334 Column has variance of  0.029888376975788052 which is very low, hence can be dropped
337 Column has variance of  2.888078659500959 which is very low, hence can be dropped
342 Column has variance of  0.00012811520819987126 which is very low, hence can be dropped
347 Column has variance of  0.12403515444586867 which is very low, hence can be dropped
348 Column has variance of  0.00014071846291313514 which is very low, hence can be dropped
349 Column has variance of  0.00011242800894042184 which is very low, hence can be dropped
350 Column has variance of  0.00020522439258338344 which is very low, hence can be dropped
351 Column has variance of  0.0006033369437810851 which is very low, hence can be dropped
352 Column has variance of  0.00017311069178995876 which is very low, hence can be dropped
353 Column has variance of  0.0002402274658072566 which is very low, hence can be dropped
354 Column has variance of  0.0001707699738411117 which is very low, hence can be dropped
355 Column has variance of  0.0004975884980494316 which is very low, hence can be dropped
356 Column has variance of  0.14970523332802896 which is very low, hence can be dropped
357 Column has variance of  2.509253001278694e-07 which is very low, hence can be dropped
359 Column has variance of  5.0927598464824974e-05 which is very low, hence can be dropped
360 Column has variance of  0.0004001027561593251 which is very low, hence can be dropped
362 Column has variance of  0.00046846512707141334 which is very low, hence can be dropped
365 Column has variance of  7.054390421872338e-06 which is very low, hence can be dropped
366 Column has variance of  5.676063644460448e-06 which is very low, hence can be dropped
367 Column has variance of  7.285035923717533e-06 which is very low, hence can be dropped
368 Column has variance of  4.4381107689022426e-06 which is very low, hence can be dropped
376 Column has variance of  2.855300000817083e-07 which is very low, hence can be dropped
377 Column has variance of  2.1765962592843768e-07 which is very low, hence can be dropped
385 Column has variance of  0.0002063712797978626 which is very low, hence can be dropped
386 Column has variance of  0.00023988228085489242 which is very low, hence can be dropped
387 Column has variance of  2.4893458691841078e-05 which is very low, hence can be dropped
389 Column has variance of  0.00013961795973955034 which is very low, hence can be dropped
391 Column has variance of  4.539670690529095e-05 which is very low, hence can be dropped
392 Column has variance of  8.73529629711132e-06 which is very low, hence can be dropped
393 Column has variance of  0.0014752123041889655 which is very low, hence can be dropped
405 Column has variance of  0.00011509577804474522 which is very low, hence can be dropped
406 Column has variance of  8.006541582696903 which is very low, hence can be dropped
407 Column has variance of  0.13301421099402128 which is very low, hence can be dropped
408 Column has variance of  6.646690706388391 which is very low, hence can be dropped
409 Column has variance of  3.157171928805614 which is very low, hence can be dropped
410 Column has variance of  4.50703532970221 which is very low, hence can be dropped
411 Column has variance of  0.30412375911765377 which is very low, hence can be dropped
416 Column has variance of  1.0721218245803485 which is very low, hence can be dropped
420 Column has variance of  9.34948205353655 which is very low, hence can be dropped
426 Column has variance of  0.991259320665041 which is very low, hence can be dropped
427 Column has variance of  9.254643130984583 which is very low, hence can be dropped
437 Column has variance of  2.5962028463559714 which is very low, hence can be dropped
441 Column has variance of  0.033934322921996614 which is very low, hence can be dropped
442 Column has variance of  0.43453746523763026 which is very low, hence can be dropped
443 Column has variance of  0.020607190357725545 which is very low, hence can be dropped
444 Column has variance of  0.024187001465470325 which is very low, hence can be dropped
445 Column has variance of  0.019952177712835424 which is very low, hence can be dropped
446 Column has variance of  0.031031714405134657 which is very low, hence can be dropped
447 Column has variance of  0.007475463626818293 which is very low, hence can be dropped
448 Column has variance of  0.05582603044177594 which is very low, hence can be dropped
452 Column has variance of  0.8449219817890223 which is very low, hence can be dropped
453 Column has variance of  5.066120575531568 which is very low, hence can be dropped
454 Column has variance of  9.361521769484813 which is very low, hence can be dropped
455 Column has variance of  0.8805422376655848 which is very low, hence can be dropped
459 Column has variance of  1.8105755198289895 which is very low, hence can be dropped
469 Column has variance of  9.933116345587658 which is very low, hence can be dropped
475 Column has variance of  6.8182295359303735 which is very low, hence can be dropped
479 Column has variance of  6.962253864646226 which is very low, hence can be dropped
491 Column has variance of  1.4988684958663911 which is very low, hence can be dropped
493 Column has variance of  0.9485752718627868 which is very low, hence can be dropped
526 Column has variance of  0.9185833359574673 which is very low, hence can be dropped
527 Column has variance of  3.5671786090389914 which is very low, hence can be dropped
539 Column has variance of  1.5697910818881597 which is very low, hence can be dropped
540 Column has variance of  0.5357190761421328 which is very low, hence can be dropped
541 Column has variance of  8.388992772650454 which is very low, hence can be dropped
542 Column has variance of  7.489852087299687e-06 which is very low, hence can be dropped
543 Column has variance of  2.3517591658972197e-06 which is very low, hence can be dropped
544 Column has variance of  8.733216214670339e-08 which is very low, hence can be dropped
545 Column has variance of  1.7306566992676808 which is very low, hence can be dropped
546 Column has variance of  0.15137220405833376 which is very low, hence can be dropped
549 Column has variance of  0.4533944972533438 which is very low, hence can be dropped
551 Column has variance of  1.8526403049429587 which is very low, hence can be dropped
552 Column has variance of  0.07630336949571859 which is very low, hence can be dropped
553 Column has variance of  4.807702119436431 which is very low, hence can be dropped
554 Column has variance of  0.35862371543244337 which is very low, hence can be dropped
556 Column has variance of  1.6384215573532654 which is very low, hence can be dropped
557 Column has variance of  3.4985212478286876 which is very low, hence can be dropped
558 Column has variance of  0.007032421964754232 which is very low, hence can be dropped
559 Column has variance of  0.04055868524944201 which is very low, hence can be dropped
560 Column has variance of  0.0026602720685329926 which is very low, hence can be dropped
563 Column has variance of  0.014824952454537492 which is very low, hence can be dropped
564 Column has variance of  6.935760827293852 which is very low, hence can be dropped
565 Column has variance of  0.006580836421564915 which is very low, hence can be dropped
566 Column has variance of  1.0665956113661326 which is very low, hence can be dropped
567 Column has variance of  0.0010732798612669973 which is very low, hence can be dropped
568 Column has variance of  0.993299610084573 which is very low, hence can be dropped
571 Column has variance of  0.07568652701397191 which is very low, hence can be dropped
573 Column has variance of  0.06174137791144954 which is very low, hence can be dropped
575 Column has variance of  0.004595635745341555 which is very low, hence can be dropped
578 Column has variance of  0.00013760017655111654 which is very low, hence can be dropped
579 Column has variance of  9.293216209553479e-05 which is very low, hence can be dropped
580 Column has variance of  9.70936772565866e-06 which is very low, hence can be dropped
582 Column has variance of  1.1589429400315796e-05 which is very low, hence can be dropped
583 Column has variance of  0.0002951496782670073 which is very low, hence can be dropped
584 Column has variance of  1.3841710146524136e-05 which is very low, hence can be dropped
586 Column has variance of  0.00015272451356909456 which is very low, hence can be dropped
587 Column has variance of  7.757267970327905e-05 which is very low, hence can be dropped
588 Column has variance of  8.220099041533564e-06 which is very low, hence can be dropped
New shape of the data set after deleting above 272  columns is (1567, 183)
In [14]:
# Now lets check how much null values do we have in our data set
Data.isnull().sum()
Out[14]:
0              6
1              7
2             14
3             14
4             14
6             14
12             2
15             3
21             2
22             2
23             2
24             2
28             2
40            24
43             1
45             1
46             1
48             1
50             1
51             1
55             4
59             7
60             6
62             6
63             7
64             7
65             7
66             6
67             6
68             6
70             6
71             6
72           794
73           794
88             0
90            51
115            0
117            0
133            8
135            5
136            6
137            7
138           14
139           14
140           14
142           14
148            2
150            3
151            3
152            3
154            3
159            2
160            2
161            2
162            2
180            1
182            1
183            1
185            1
187            1
188            1
196            7
197            6
199            6
200            7
201            7
202            7
203            6
204            6
205            6
207            6
208            6
223            0
225           51
250            0
252            0
268            8
270            5
271            6
272            7
273           14
274           14
275           14
283            2
286            3
287            3
294            2
295            2
296            2
297            2
324            1
332            7
333            6
335            6
336            7
338            7
339            6
340            6
341            6
343            6
344            6
345          794
346          794
361            0
363           51
388            0
390            0
412           14
413           14
415           14
417            2
418            2
419            2
421            2
423            3
424            3
425            3
428           10
429            0
430            2
431            2
432            2
433            2
434            2
435            2
436            2
438            2
439            2
440            2
456            1
457            1
460            1
467            4
468            7
470            6
471            6
472            7
473            7
474            7
476            6
477            6
478            6
480            6
482           24
483           24
484           24
485           24
486           24
487           24
488           24
489           24
490            1
494            0
495            0
496           51
497           51
499            2
500            2
510            2
511            2
519          715
520            0
521            0
522            0
523            0
524            0
525           24
547          260
548          260
550          260
555          260
561            1
562          273
569          273
570            0
572            0
574            0
576            0
577            0
581          949
585            1
589            1
Pass/Fail      0
dtype: int64
In [15]:
Data.isna().sum().sum()
# so we have total of 7585 null values across 183 columns
Out[15]:
7585
In [16]:
# Since we do not have domain expertise on each particular feature, we will fill the null values with the mean value 

#Replace blank valus with Nan values
Data = Data.replace('', np.nan)

#Replace the Null value with the mean value of each column
for columns in Data.columns:
    mean = Data[columns].mean()
    Data[columns] = Data[columns].fillna(mean)
In [17]:
#Lets check null values again
Data.isnull().sum().sum()
Out[17]:
0
In [18]:
# now that we have our base data ready, lets perform Data analysis & visualisation
#Lets check the distribution of each feature
Data.hist(color='lightblue', edgecolor = 'black', alpha = 0.7, figsize = (20,20), layout=(37,5))
plt.tight_layout()
plt.show()
In [19]:
Data.skew()
# We can see that except for below mentioned columns rest all columns are highly skewed
Out[19]:
0             0.514641
1            -0.043163
2            -0.307136
3             1.719310
4            19.733442
6            -0.107427
12            7.209324
15           17.076921
21            2.376138
22           -2.182923
23            0.356874
24           -0.054125
28           -0.063702
40           -1.882466
43            0.554674
45            0.374818
46            0.337946
48           -0.019920
50            0.389282
51           -0.509794
55            0.368893
59            4.730023
60            0.314994
62            5.307243
63           10.706091
64            1.130865
65            3.333722
66           -0.204512
67           20.824463
68           -2.902413
70            0.758319
71            1.254421
72           -9.774366
73           14.111827
88           -0.272824
90            0.347334
115          -0.271651
117          38.005963
133          -0.277546
135           6.192576
136           0.333026
137           0.384090
138           0.823306
139           2.085160
140          19.735009
142          15.039760
148          38.562024
150           1.296333
151          13.005347
152          39.557423
154          27.732438
159           4.206303
160           3.995751
161           2.231207
162           1.829927
180           0.776498
182           2.144810
183           0.201764
185          30.709184
187          24.516484
188           0.766068
196          17.393147
197          16.253846
199          14.588119
200          13.439685
201           9.746788
202          24.733026
203          17.573474
204          17.634821
205          17.887940
207          18.237948
208           0.162865
223          17.146330
225           1.091511
250           6.751706
252          39.560364
268           0.578674
270           5.175073
271           0.348704
272           0.346599
273           1.002222
274           2.178885
275          19.735004
283          38.647193
286          13.968135
287          39.559150
294           4.429284
295           4.224084
296           2.190904
297           1.791628
324           0.706663
332          22.774616
333          18.659509
335          20.293567
336          19.114061
338          27.894916
339          22.019652
340          18.269609
341          17.895266
343          20.570310
344           0.171990
345          12.530000
346          11.243294
361          16.868775
363           1.000129
388           6.285941
390          39.562779
412           1.816378
413          16.359941
415          16.283884
417           2.495089
418           0.456661
419           0.499839
421          37.696746
423           2.084869
424          12.625177
425          36.258005
428           9.207376
429          20.552274
430           7.394316
431           7.103304
432           3.346368
433           1.364392
434           8.543970
435           8.665764
436           8.698782
438          10.164666
439           6.757087
440           0.117124
456          15.791705
457          27.827277
460           1.867412
467          10.454602
468           1.262658
470           8.624263
471          10.642803
472           0.574882
473           3.435317
474           5.466532
476           5.458772
477          19.787756
478          39.585205
480           0.815464
482           0.469546
483           1.714218
484           1.534042
485           1.524456
486           0.615203
487           1.160917
488           0.356705
489           1.047157
490           0.908301
494          16.161844
495          19.099472
496           3.280515
497           1.083132
499           0.743494
500           0.920019
510           4.109312
511           0.700040
519           5.525019
520          17.415222
521           9.040238
522           5.218409
523          21.906221
524          38.854591
525          14.046365
547          -0.452326
548           0.938833
550          13.098494
555           1.924065
561           0.805957
562           0.116481
569           2.256412
570          -8.658927
572           4.298821
574           4.294132
576           4.195898
577           4.169820
581           4.710143
585          24.705005
589           2.715340
Pass/Fail     3.487359
dtype: float64
In [20]:
for columns in Data.columns:
    if Data[columns].skew() <= 0.5 and Data[columns].skew() >= -0.5:
        print( columns , 'column is close to normal distribution with', Data[columns].skew(), 'skewness') 
1 column is close to normal distribution with -0.04316264649515132 skewness
2 column is close to normal distribution with -0.3071360279896156 skewness
6 column is close to normal distribution with -0.10742686096931855 skewness
23 column is close to normal distribution with 0.35687433333104274 skewness
24 column is close to normal distribution with -0.05412523101217642 skewness
28 column is close to normal distribution with -0.06370154039777466 skewness
45 column is close to normal distribution with 0.3748180652355466 skewness
46 column is close to normal distribution with 0.33794574731566174 skewness
48 column is close to normal distribution with -0.019919872092288217 skewness
50 column is close to normal distribution with 0.38928231336840213 skewness
55 column is close to normal distribution with 0.3688928821847343 skewness
60 column is close to normal distribution with 0.3149941060125438 skewness
66 column is close to normal distribution with -0.2045121899230426 skewness
88 column is close to normal distribution with -0.27282399081128983 skewness
90 column is close to normal distribution with 0.34733443776774076 skewness
115 column is close to normal distribution with -0.27165065863283777 skewness
133 column is close to normal distribution with -0.27754598654909324 skewness
136 column is close to normal distribution with 0.3330260984322855 skewness
137 column is close to normal distribution with 0.3840900389944301 skewness
183 column is close to normal distribution with 0.20176425747939875 skewness
208 column is close to normal distribution with 0.16286496147345517 skewness
271 column is close to normal distribution with 0.3487037100911712 skewness
272 column is close to normal distribution with 0.34659948108345867 skewness
344 column is close to normal distribution with 0.17198993560941542 skewness
418 column is close to normal distribution with 0.4566608966307543 skewness
419 column is close to normal distribution with 0.4998388672079762 skewness
440 column is close to normal distribution with 0.11712380906663562 skewness
482 column is close to normal distribution with 0.4695460556312447 skewness
488 column is close to normal distribution with 0.35670526829994803 skewness
547 column is close to normal distribution with -0.452326402218069 skewness
562 column is close to normal distribution with 0.11648141179240548 skewness
In [21]:
#Lets check for the outliers in thh dataset
for columns in Data.columns:
    plt.figure()
    plt.title(columns)
    sns.boxplot(data = Data[columns], orient="h" , color = 'pink')

Since we have Outliers present in almost all the columns, changing all the values to adjust outliers in all the columns will change the entire data set. ALso, we have features with only negative values, hence taking log transformation will result in undifined values (NAN). Hence in this data set, we will prefer keeping data set untouched w.r.t outliers, (However with agreement with SME, we can still choose to take care of outliers)

In [22]:
#for correlation, closer the value to 1, higher is the corelation betwen two features
Data.corr()
Out[22]:
0 1 2 3 4 6 12 15 21 22 23 24 28 40 43 45 46 48 50 51 55 59 60 62 63 64 65 66 67 68 70 71 72 73 88 90 115 117 133 135 136 137 138 139 140 142 148 150 151 152 154 159 160 161 162 180 182 183 185 187 188 196 197 199 200 201 202 203 204 205 207 208 223 225 250 252 268 270 271 272 273 274 275 283 286 287 294 295 296 297 324 332 333 335 336 338 339 340 341 343 344 345 346 361 363 388 390 412 413 415 417 418 419 421 423 424 425 428 429 430 431 432 433 434 435 436 438 439 440 456 457 460 467 468 470 471 472 473 474 476 477 478 480 482 483 484 485 486 487 488 489 490 494 495 496 497 499 500 510 511 519 520 521 522 523 524 525 547 548 550 555 561 562 569 570 572 574 576 577 581 585 589 Pass/Fail
0 1.000000 -0.143840 0.004756 -0.007613 -0.011014 0.002270 0.010368 0.030675 -0.011075 0.032206 -0.046678 -0.014921 0.054548 -0.009150 -0.050244 0.015586 -0.006066 0.004240 -0.019867 -0.050817 -0.024957 -0.105184 -0.036578 0.008042 -0.045524 -0.017521 -0.019591 -0.000433 -0.023074 0.033390 -0.001325 -0.000247 -0.003495 0.008029 -0.029554 0.012107 0.023283 -0.000732 -0.007950 -0.070572 0.157770 0.160297 -0.021708 0.001720 -0.011107 -0.007485 0.000533 0.006545 -0.014213 0.003507 -0.009449 -0.037011 -0.003787 0.014089 0.063448 -0.002006 0.030302 -0.023634 -0.006813 -0.013009 -0.046557 -0.023397 -0.019154 -0.016829 -0.029920 0.000113 -0.017513 -0.024940 -0.027469 -0.032856 -0.029298 -0.038483 -0.023147 -0.015300 0.008180 -0.004230 -0.024374 -0.069232 0.155582 0.151401 -0.012819 0.004790 -0.011100 0.001747 -0.018155 0.003504 -0.038470 -0.009218 0.013929 0.060713 -0.037667 -0.022557 -0.016478 -0.017414 -0.023233 -0.022272 -0.024616 -0.023229 -0.031396 -0.025620 -0.036954 0.000941 -0.002220 -0.022630 -0.029094 -0.000282 -0.004340 0.007662 -0.022543 -0.007946 0.030384 -0.002017 0.016435 -0.001046 0.026659 -0.029941 -0.007224 0.004678 0.039119 -0.056194 -0.041317 -0.010828 0.062605 -0.064344 -0.065386 -0.064745 0.026556 0.032202 0.050793 0.015557 -0.006110 0.003927 0.021150 0.053943 -0.026841 -0.010854 0.013495 0.023699 0.004028 -0.019361 -0.031410 -0.029400 -0.036717 -0.011355 0.048705 -0.015355 -0.023708 -0.033258 0.076663 0.060053 -0.028320 -0.011895 -0.023695 -0.021992 0.002052 -0.017511 -0.051050 -0.019014 -0.062474 -0.018555 -0.039162 -0.011748 0.014244 0.003531 0.000986 -0.004357 -0.011434 0.027381 -0.089448 -0.075674 0.030640 0.037917 -0.009583 0.049862 -0.018953 0.013678 0.015206 0.013228 0.008601 -0.017120 0.023589 0.004174 -0.025141
1 -0.143840 1.000000 0.005767 -0.007568 -0.001636 -0.025564 0.034062 -0.087315 0.058155 -0.052664 -0.016047 -0.060066 -0.022847 0.027101 -0.019848 0.017935 0.007923 0.005573 0.004888 0.022586 0.017092 0.007505 -0.035006 -0.013760 0.038595 0.058949 0.054413 -0.020000 0.002643 0.018941 -0.026117 -0.018276 -0.012443 -0.001506 -0.007194 0.019660 0.029167 -0.009297 -0.034737 0.051456 -0.031967 -0.113532 -0.030106 0.009966 -0.001786 0.028495 0.001703 -0.044156 -0.097923 -0.004628 0.018289 0.037930 0.029999 0.037932 -0.005155 -0.030468 0.004351 -0.007852 0.005508 0.003371 0.056727 0.003240 -0.002687 0.009757 -0.001837 0.005695 0.008953 -0.006723 0.002100 0.007972 -0.006351 -0.066794 -0.021081 0.038764 0.010467 -0.003781 0.055382 0.041599 -0.035679 -0.110727 -0.020571 0.009278 -0.001783 0.001968 -0.093081 -0.004637 0.040675 0.033998 0.036893 -0.005201 0.048492 0.004168 -0.000372 0.011866 0.007823 0.009072 -0.005718 0.001792 0.008263 -0.008455 -0.057460 0.001949 0.006292 -0.016832 0.043958 0.016542 -0.003942 0.019433 0.005295 0.027474 0.027260 0.043736 -0.023114 0.003700 -0.007353 -0.092269 -0.001941 0.002079 0.001136 0.049959 0.049177 0.032311 -0.001006 0.050409 0.053605 0.052811 0.024841 -0.011154 0.020194 0.008012 0.001850 0.041014 0.039161 -0.029422 0.022069 0.014448 -0.050559 -0.016558 -0.009430 -0.018242 0.003229 0.002838 -0.059279 0.024601 -0.027730 -0.049265 -0.013099 0.011614 -0.003226 0.002316 0.010647 -0.020355 0.019295 -0.018646 0.015467 0.037509 -0.001513 0.005301 0.018804 0.032532 0.010311 -0.004022 0.042952 0.009682 -0.005029 -0.007876 0.068595 0.034569 0.070026 0.026976 -0.024335 -0.025492 0.037138 -0.025490 -0.009000 0.001753 0.001303 0.002570 -0.010145 0.054006 0.002273 0.044797 -0.002603
2 0.004756 0.005767 1.000000 0.298935 0.095891 -0.136225 0.018326 0.006115 0.044468 -0.029830 0.009276 -0.021149 -0.061725 -0.014761 0.050536 0.005874 0.010206 -0.096163 -0.008547 -0.016448 -0.008088 0.039710 0.039177 -0.013211 -0.028692 0.007603 0.014053 0.001573 -0.013251 -0.022889 0.002973 0.053692 0.008350 -0.003914 0.000507 0.040394 0.039054 0.021111 -0.015685 -0.010705 0.051600 0.047842 0.272222 0.021581 0.095947 0.006404 0.015360 0.003297 0.003101 0.018247 0.008429 0.015631 0.012170 -0.031203 -0.059200 -0.017295 -0.019236 -0.046624 0.016055 -0.020921 0.001435 -0.020661 -0.017141 -0.034084 -0.006726 -0.022558 0.002079 -0.010616 -0.002809 -0.019800 -0.009537 -0.029961 0.016448 0.047563 0.018057 0.015614 -0.086716 -0.022980 0.053480 0.046357 0.168825 0.029334 0.095882 0.016481 0.007158 0.018239 0.017878 0.013097 -0.028628 -0.056396 0.000057 -0.020073 -0.010751 -0.030948 -0.023989 0.013134 -0.003215 -0.008152 -0.019603 -0.010406 -0.035011 -0.006335 -0.001214 0.010095 0.054482 0.020565 0.015703 -0.124758 0.107609 0.028089 0.048093 -0.013755 0.021395 0.014566 -0.003459 0.007356 0.028664 0.029698 0.008704 0.023505 0.022954 0.018743 -0.018969 0.022694 0.025098 0.025229 -0.074651 -0.058467 -0.020019 -0.000669 0.021667 0.013232 -0.038047 -0.073040 0.004692 -0.034835 -0.007182 -0.033182 -0.052553 -0.045830 -0.023197 0.030657 -0.045635 -0.024090 -0.032611 -0.009574 0.012172 -0.004345 0.007753 0.021461 -0.023853 0.003173 -0.007174 0.014202 0.048647 0.043351 0.004401 -0.005940 0.017035 0.063829 0.062442 -0.023720 -0.020388 0.013516 -0.029512 0.014930 -0.005911 0.028152 -0.026891 0.017110 -0.004217 0.025862 0.013310 0.064282 -0.037070 -0.000518 0.001342 0.002592 -0.028705 -0.007054 0.015752 -0.032890 -0.000957
3 -0.007613 -0.007568 0.298935 1.000000 -0.058483 -0.685835 -0.028223 -0.013157 0.021111 -0.033141 -0.007973 -0.049605 0.096876 -0.006463 -0.023326 -0.031329 -0.043089 -0.021524 -0.056539 -0.012499 -0.016235 -0.020691 -0.025746 -0.007548 -0.032560 -0.026986 -0.028134 -0.027224 0.009517 0.017397 -0.015267 0.083641 -0.002320 0.009338 -0.016283 -0.007633 -0.002689 0.037765 0.000703 0.051198 0.021363 -0.006539 -0.206134 0.299731 -0.059719 -0.073778 0.008853 -0.045914 -0.005321 0.007937 0.013438 -0.051199 -0.076747 -0.010054 0.041761 0.070750 0.022531 -0.020704 -0.002026 0.008143 -0.029602 0.000590 0.009206 0.016457 0.007700 -0.006193 0.014087 0.004216 0.012983 -0.004443 0.016520 -0.020699 0.012984 -0.030584 -0.040013 0.039671 -0.132485 0.054943 0.009293 -0.010670 -0.329403 0.307743 -0.059730 0.008141 -0.004497 0.007916 -0.053258 -0.074885 -0.013636 0.041969 -0.026751 0.006240 0.012213 0.019793 0.013443 0.014130 0.012932 0.012014 0.000108 0.023550 -0.022470 0.015632 0.009595 0.009297 -0.035444 -0.047899 0.039578 -0.182968 0.009818 0.005119 0.024687 -0.003754 0.033285 0.009323 -0.018230 -0.005952 0.008997 -0.031119 -0.003746 -0.043869 -0.056951 0.053350 0.017265 -0.041670 -0.035809 -0.044270 -0.008226 0.021093 0.070096 -0.022014 -0.001728 -0.015767 -0.006049 0.014881 0.026988 0.018025 0.055073 0.000456 0.028147 -0.024778 -0.003181 0.008685 -0.072706 0.030013 0.026909 -0.054647 -0.010999 0.001386 0.066520 0.009441 -0.030502 -0.044634 -0.019733 0.011414 0.010987 -0.029903 0.008492 0.017704 -0.079904 -0.019613 -0.008699 -0.032959 -0.019964 -0.040648 0.031870 0.040860 -0.007854 -0.051045 -0.066744 -0.021563 -0.060972 0.014912 0.043271 0.046434 0.002231 0.007634 0.006822 0.008216 0.016438 -0.071311 0.026019 -0.080341 -0.024623
4 -0.011014 -0.001636 0.095891 -0.058483 1.000000 -0.074368 -0.002707 0.011435 0.008353 -0.007773 0.004969 -0.013636 0.007753 0.025844 -0.012074 0.057947 0.047234 -0.028014 0.029248 0.006774 -0.052408 -0.020577 -0.008334 0.049400 -0.004640 0.002791 0.006155 0.045359 -0.002948 -0.016026 0.032287 0.037397 0.004717 -0.002216 -0.006984 -0.013718 0.012677 -0.004841 -0.047460 -0.020532 0.010716 0.004287 0.193495 0.006466 0.999975 0.667794 0.000583 -0.034916 -0.002010 -0.001580 0.006871 -0.001934 -0.002558 -0.017138 -0.017504 -0.002981 -0.013424 -0.013929 0.008997 0.000571 0.009328 0.005597 -0.005887 0.001512 -0.000862 0.025928 0.008611 -0.000232 -0.003064 -0.006370 0.004245 -0.004920 -0.010286 0.012493 0.009458 -0.000519 -0.012915 -0.025923 0.013104 0.008211 0.223024 0.035670 0.999976 0.000674 -0.002031 -0.001547 -0.003336 -0.000639 -0.019247 -0.016190 0.010048 0.004425 -0.006581 0.000463 -0.002010 0.005443 0.002815 -0.003091 -0.003335 0.006442 -0.004209 -0.000780 -0.004176 -0.005553 0.023229 0.017901 -0.000674 0.028328 0.938416 0.683776 0.001143 -0.020321 -0.008230 0.001204 -0.032696 -0.002047 -0.006193 -0.005514 -0.009466 -0.004403 -0.003564 -0.010965 0.020404 -0.005190 -0.006646 -0.006298 0.024303 0.031524 0.040941 -0.002249 0.012034 0.010376 -0.000094 0.026172 0.002907 -0.000615 -0.004844 0.028104 0.014844 -0.015896 -0.005290 -0.000981 -0.024783 -0.031177 -0.027321 -0.013163 0.017334 0.021910 0.010670 0.021383 0.020535 -0.001803 -0.005038 -0.008903 0.002687 0.014237 0.004433 0.004379 -0.002970 -0.005096 -0.000064 -0.003555 -0.005631 0.008843 0.007522 0.001458 -0.012081 -0.011498 -0.046330 0.005220 -0.022289 -0.025806 0.041957 0.027696 0.005273 -0.012024 -0.012264 -0.012163 -0.004070 0.088167 -0.001616 0.050910 -0.013756
6 0.002270 -0.025564 -0.136225 -0.685835 -0.074368 1.000000 0.058982 0.039815 -0.021131 0.035590 0.013043 0.057480 -0.107400 0.014575 0.011003 0.029945 0.030622 0.026156 0.048818 0.053057 0.013190 0.057800 0.017097 0.053272 0.030469 -0.020330 -0.003449 0.037892 0.017830 -0.054700 0.034194 -0.098829 0.009504 -0.003609 0.042190 -0.004335 -0.024270 -0.035948 -0.014152 -0.034496 -0.025010 0.006138 0.192320 -0.418355 -0.073462 -0.160978 0.018170 0.079507 -0.010553 0.027789 -0.003361 0.045314 0.055111 -0.009556 -0.090384 -0.087154 0.028125 0.026140 0.002745 -0.022264 0.041824 0.009720 0.022308 0.012430 -0.023806 -0.015873 -0.032401 -0.019459 0.000543 0.048276 -0.003503 0.037775 -0.011004 0.012131 0.023796 -0.041630 0.094769 -0.040559 -0.022838 0.008511 0.168446 -0.428265 -0.073466 0.019484 -0.016178 0.027787 0.047652 0.051698 -0.002760 -0.093579 0.038605 0.013940 0.021404 0.015709 0.018597 -0.032709 -0.030489 0.008566 0.044915 -0.006197 0.044044 -0.001735 -0.003158 -0.010266 0.022900 0.031070 -0.041378 -0.104900 -0.056450 -0.254698 -0.043188 -0.003964 -0.062485 0.014584 0.036852 -0.017212 0.036069 0.006708 0.011353 0.043572 0.048542 -0.017815 -0.042839 0.043919 0.036880 0.043969 -0.014556 -0.041655 -0.089987 -0.002236 0.002068 -0.018401 0.005001 -0.046208 0.041540 0.002904 -0.041647 0.004549 -0.027779 0.066205 0.043670 -0.043555 0.090244 -0.016502 -0.042417 0.026113 0.022466 0.029242 -0.067299 -0.025759 0.030266 0.039039 0.019779 -0.012311 -0.024347 0.011930 -0.010517 -0.035984 0.060425 0.030146 0.007628 0.014542 -0.009547 0.025062 -0.012695 -0.043822 0.002541 0.048668 0.070215 0.016154 0.066665 -0.041082 -0.046295 -0.070722 0.017264 0.009292 0.007783 0.007409 -0.012342 0.042446 -0.039517 0.043777 0.016239
12 0.010368 0.034062 0.018326 -0.028223 -0.002707 0.058982 1.000000 -0.033933 -0.061068 0.084746 -0.039963 0.047038 0.004407 0.021971 0.027272 -0.033722 -0.020290 -0.011594 -0.017019 -0.017528 0.027789 0.022526 0.005014 -0.011988 -0.013395 -0.039679 -0.045253 0.008773 -0.003563 -0.009888 -0.012357 -0.030585 -0.021080 0.012966 0.037838 0.006241 -0.020492 0.022255 -0.007097 0.022016 -0.054659 -0.005752 -0.007246 -0.045257 -0.002487 -0.001815 0.560274 0.004327 -0.039126 0.559761 0.512987 -0.026613 0.024142 -0.016556 -0.013467 0.000753 0.007994 0.005434 0.018045 0.007281 -0.015951 -0.022183 0.001834 -0.012074 -0.020370 -0.055341 -0.041238 -0.027686 -0.012369 -0.007796 -0.022881 -0.021682 -0.006252 -0.017073 0.001551 0.022686 0.007846 0.006445 -0.053940 -0.015085 -0.020028 -0.046890 -0.002501 0.563988 -0.041237 0.559760 -0.028247 0.019128 -0.017705 -0.012163 -0.015421 -0.015646 0.001891 -0.008991 -0.005033 -0.034137 -0.029310 -0.008093 -0.006452 -0.019502 -0.026168 -0.001575 -0.001708 -0.010490 -0.015058 -0.005990 0.022736 -0.038032 -0.011440 -0.009102 -0.055692 -0.005958 0.008314 0.551234 0.009568 -0.036748 0.542941 0.050897 0.031105 -0.033226 -0.009461 -0.045017 -0.049532 -0.032291 -0.032221 -0.031404 0.004300 -0.002819 -0.054285 0.010837 0.019641 -0.003256 0.006161 -0.020666 -0.023138 -0.013665 -0.008107 -0.037111 -0.040754 0.028069 -0.008589 -0.025749 0.018050 0.014685 -0.038991 0.055404 0.025057 -0.015412 -0.014044 0.035711 0.053359 -0.017719 -0.022577 -0.008136 0.003849 -0.017645 -0.009372 0.000123 -0.001157 -0.011431 0.000133 0.001144 -0.022790 0.001711 0.015141 0.023988 0.019349 0.020488 0.059876 -0.004345 0.044070 -0.027928 0.015934 -0.007246 -0.000639 0.036757 0.032908 0.035743 0.031434 -0.038481 0.000523 -0.036720 -0.005969
15 0.030675 -0.087315 0.006115 -0.013157 0.011435 0.039815 -0.033933 1.000000 0.001786 -0.002054 -0.021383 0.022276 0.018212 0.006769 0.024793 -0.000303 0.018156 0.013455 0.024650 0.026860 0.005856 0.022178 0.034017 0.023657 -0.005630 -0.037096 0.019487 0.006020 0.009494 -0.037605 0.027683 -0.029459 0.007532 -0.001884 0.036382 0.019760 0.028784 -0.016883 -0.017014 0.001615 0.023437 0.034874 -0.022190 -0.018498 0.011280 -0.011268 -0.012967 0.147330 0.479135 -0.010243 -0.020257 -0.008665 -0.037638 0.020081 0.032913 -0.007347 0.029576 -0.000074 -0.005318 0.011640 0.021117 0.050464 0.021682 0.046948 0.065260 0.089866 0.116357 0.089023 0.060010 0.051900 0.051737 -0.016114 0.006374 0.011028 -0.007850 -0.014996 0.043453 0.011273 0.024291 0.042403 -0.017674 -0.022461 0.011275 -0.013094 0.470048 -0.010334 -0.009648 -0.036574 0.016652 0.037962 0.015857 0.027074 0.015430 0.024519 0.028727 0.119924 0.098197 0.039041 0.042530 0.035008 -0.010450 0.008070 0.019806 0.020726 0.017922 -0.000749 -0.014789 -0.020993 -0.002345 -0.010814 0.029856 0.005642 0.021455 -0.013376 0.252881 0.323039 -0.001929 0.000438 -0.003696 -0.012381 -0.026910 0.013698 0.048543 -0.013601 -0.012784 -0.016001 0.025876 -0.013699 0.029563 -0.011621 -0.006639 -0.000904 0.002745 -0.010736 0.023597 0.064624 0.041329 0.073615 0.060787 0.017147 0.042255 0.134922 0.011658 -0.036588 -0.030424 0.002007 0.005349 -0.017061 -0.003285 0.001814 -0.006037 -0.019630 0.020435 0.003807 0.013484 0.007563 0.010213 -0.035410 0.000543 -0.000151 -0.002565 0.005861 0.000592 -0.012267 -0.000763 -0.013476 -0.005306 0.030121 0.019602 -0.023780 -0.011686 -0.044469 -0.047842 0.000864 0.011928 -0.024789 -0.024032 -0.023509 -0.019152 0.014444 0.017745 0.009764 -0.002884
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577 0.008601 -0.010145 -0.028705 0.016438 -0.004070 -0.012342 0.031434 -0.019152 0.045633 -0.021553 0.010524 -0.017735 0.065944 0.014344 -0.003703 0.014711 0.016525 0.015873 0.018995 -0.044813 0.023538 -0.023120 -0.015284 0.019960 0.031031 0.028122 0.022238 0.015829 0.063675 0.012991 0.014073 -0.039950 -0.081573 0.092446 -0.021203 0.023878 0.041202 -0.006304 -0.017026 0.003526 0.006406 0.000589 -0.034490 -0.018248 -0.004565 -0.034469 0.010378 -0.029066 -0.008026 0.009790 0.008336 0.005171 0.006583 -0.020128 0.017535 0.046162 0.015104 -0.062275 0.010687 -0.030143 0.004576 0.044501 0.058738 0.052162 0.029529 0.021649 0.031994 0.023056 0.055704 0.041874 0.029620 -0.017079 0.004871 0.016646 0.004559 -0.008353 -0.003158 -0.006639 -0.001612 -0.003953 -0.040836 -0.023427 -0.004565 0.010066 -0.008002 0.009765 0.006173 0.011868 -0.024745 0.013454 0.011059 0.047569 0.064696 0.053736 0.046935 0.033539 0.018160 0.062642 0.047379 0.031907 -0.009877 0.085314 0.090903 0.012923 0.011182 0.004772 -0.008538 -0.026105 -0.005433 -0.027959 0.060940 0.023594 0.012381 0.010003 -0.041999 -0.008789 0.004074 -0.024946 0.031586 0.000788 -0.002707 -0.013394 0.058159 -0.005972 -0.006166 -0.004664 0.003241 0.080274 0.073433 0.038838 0.013113 0.078919 0.145196 0.013074 0.041267 0.051678 -0.018503 0.009461 0.028519 -0.015440 0.039447 -0.008827 -0.031360 0.023542 0.060684 0.026602 0.028648 0.022420 0.067747 0.040015 -0.023596 -0.010476 -0.020297 0.006519 0.005756 0.013395 0.010447 -0.032501 -0.064290 -0.057921 0.001115 -0.009651 -0.002178 -0.000141 -0.012852 -0.009246 -0.007812 -0.025458 -0.052203 -0.022278 -0.060659 -0.052455 0.023153 -0.009732 -0.247655 0.863768 0.851784 0.859278 1.000000 -0.009745 -0.023910 -0.024766 -0.049633
581 -0.017120 0.054006 -0.007054 -0.071311 0.088167 0.042446 -0.038481 0.014444 -0.013449 -0.030599 -0.014964 0.004892 -0.005684 -0.050235 0.049381 0.055536 0.070753 -0.037160 0.066597 0.008090 0.028175 -0.024339 0.062491 0.020490 -0.025566 0.032081 0.005661 0.068390 -0.014739 0.047279 0.079040 0.084174 0.032663 -0.023746 0.021523 0.040042 0.113359 -0.014041 -0.086257 -0.005461 0.023882 -0.007996 -0.007293 -0.017651 0.088316 0.132325 -0.000877 0.032126 0.001699 0.001700 -0.006966 0.030538 0.023542 0.027488 -0.001550 0.025069 0.026616 -0.025730 0.014553 -0.018201 0.008740 -0.015554 -0.013579 -0.018222 -0.052761 -0.011346 -0.016707 -0.038164 -0.012580 -0.009575 -0.027124 -0.016115 0.048860 0.036622 0.082655 -0.024019 -0.010013 -0.010013 0.017618 -0.000647 0.013826 -0.023399 0.088322 -0.001280 0.000686 0.001825 0.033562 0.025810 0.029577 -0.008810 0.008965 -0.014621 -0.017959 -0.016671 -0.017854 -0.014780 -0.034873 -0.013715 -0.009651 -0.027568 -0.008305 -0.022426 -0.021490 0.057954 0.044492 0.090553 -0.023920 0.003536 0.082179 0.131296 0.029608 0.017497 0.000425 -0.000842 0.006998 0.001176 0.018890 -0.015555 0.021782 0.043900 0.045770 -0.000245 0.012365 0.045354 0.046341 0.048985 -0.011265 -0.010737 -0.025780 0.000346 0.018000 -0.009663 -0.001254 0.009232 -0.001237 -0.020401 -0.009976 -0.017321 -0.006029 -0.027197 -0.010881 0.000069 -0.034135 -0.036335 0.040059 -0.077548 0.023266 0.049260 0.005895 -0.018649 0.034226 0.007107 0.012716 0.046968 0.014671 0.032639 0.013135 0.026238 0.022443 0.043442 -0.010712 0.045955 -0.015159 0.062489 -0.021175 -0.026980 0.047599 0.023380 -0.007122 0.000251 -0.017285 0.003698 -0.011938 -0.017344 0.011714 -0.012384 -0.011594 -0.012419 -0.009745 1.000000 -0.000471 0.585288 -0.013601
585 0.023589 0.002273 0.015752 0.026019 -0.001616 -0.039517 0.000523 0.017745 -0.002637 -0.008558 -0.002240 -0.010149 -0.036787 0.007846 -0.000745 0.105375 0.097681 -0.020736 0.084296 -0.004932 0.010061 -0.027998 0.006072 0.071689 0.012442 0.047657 0.049965 0.072824 0.009573 -0.005903 0.066044 -0.000381 0.004822 -0.003146 -0.009127 0.005146 0.010785 -0.008152 -0.032886 0.002639 0.006032 -0.011129 -0.025242 -0.004993 -0.002017 -0.036200 0.005805 0.002338 0.000615 -0.000068 0.021361 0.057848 -0.007748 -0.021092 -0.017733 -0.051166 0.024443 0.038999 -0.006741 0.024482 0.005484 0.011361 -0.005643 0.017493 0.001461 0.022453 0.007852 0.006587 0.007178 0.003759 0.002861 0.043542 -0.011547 0.000029 0.002583 -0.005399 -0.000598 0.008659 0.014139 0.002212 -0.027947 -0.008326 -0.002015 0.005081 -0.000487 -0.000058 0.050509 -0.007382 -0.020954 -0.017163 0.005600 0.005323 -0.003708 0.010814 0.008062 0.005178 0.003995 0.008340 0.006706 0.000406 0.031904 -0.003688 -0.001741 -0.016836 0.004501 0.011482 -0.005486 -0.017850 -0.001422 -0.030134 -0.017273 -0.027024 0.000457 0.007777 -0.005335 -0.001079 0.000673 -0.010985 0.004082 0.023100 -0.009110 -0.013933 -0.019441 -0.004271 -0.007680 -0.006692 -0.022548 -0.026866 0.026093 0.004392 -0.008347 -0.006414 -0.003953 -0.001777 0.021418 0.018212 -0.023390 0.005076 -0.001499 0.023803 0.006728 -0.001669 0.036367 0.001089 0.001931 0.015514 -0.003509 -0.032172 0.023124 0.014772 0.027997 0.029287 -0.010933 -0.009952 0.057347 -0.001534 -0.024889 -0.031075 0.026216 -0.026200 -0.002231 0.008395 -0.005138 0.000488 0.003167 -0.003234 -0.012298 -0.021702 0.006251 0.004231 0.026898 0.023803 -0.010457 0.055153 0.010143 -0.017179 -0.016812 -0.017147 -0.023910 -0.000471 1.000000 -0.003800 0.005034
589 0.004174 0.044797 -0.032890 -0.080341 0.050910 0.043777 -0.036720 0.009764 -0.030761 0.004419 -0.037950 -0.016735 -0.085175 -0.060163 0.079700 0.017425 0.054831 -0.009350 0.068414 0.003419 0.080610 0.042628 0.065373 0.011885 0.049805 0.045951 0.062864 0.022853 0.025468 0.013833 0.059547 0.040782 0.003765 -0.001901 0.035732 0.034887 0.063218 -0.012075 -0.080567 -0.015311 0.010788 -0.016306 -0.007951 -0.044007 0.050909 0.071705 -0.025198 0.013957 0.052482 -0.025900 -0.020997 0.037101 0.012282 0.008285 -0.030163 0.026381 0.030697 -0.047126 0.020697 -0.025498 0.037813 0.071597 0.053303 0.051722 0.027411 0.063565 0.091914 0.064418 0.062954 0.058584 0.057852 -0.002409 0.023060 0.038228 0.060942 -0.013656 -0.031775 -0.031872 0.007797 -0.005934 0.027428 -0.045997 0.050924 -0.024268 0.064870 -0.025821 0.040391 0.015086 0.011792 -0.035133 0.032077 0.060694 0.041811 0.044236 0.043967 0.099258 0.075016 0.043262 0.053464 0.044773 0.008217 0.061612 0.064424 0.027144 0.039242 0.064612 -0.013516 -0.017308 0.052294 0.070211 0.026880 0.009326 0.028031 -0.024310 -0.046007 0.054917 -0.016578 -0.002560 0.009502 0.045654 0.034040 -0.016258 -0.014079 0.044799 0.044365 0.046530 -0.056559 -0.072155 -0.056109 0.049000 0.024707 0.047633 -0.005916 -0.020457 0.045506 0.052503 -0.018694 0.025195 0.040092 -0.026838 0.052179 0.120153 -0.021253 -0.010267 0.013663 -0.071487 -0.018679 0.034406 -0.012958 -0.010217 -0.007881 0.015704 0.026163 0.020640 0.021782 0.034176 0.017603 -0.002092 0.026100 0.049598 0.013606 0.041534 0.033088 0.049890 0.011418 -0.011418 0.057244 0.037897 0.033783 0.030325 -0.027873 0.020439 -0.025276 -0.016591 -0.010583 -0.022672 -0.020471 -0.022567 -0.024766 0.585288 -0.003800 1.000000 -0.002653
Pass/Fail -0.025141 -0.002603 -0.000957 -0.024623 -0.013756 0.016239 -0.005969 -0.002884 0.107997 -0.073380 0.012873 -0.018297 -0.106767 -0.051763 -0.020470 0.008347 -0.009413 -0.015267 -0.015175 0.006005 -0.008948 0.155771 -0.018342 -0.019012 0.059912 0.076551 0.054817 -0.039026 0.039532 -0.052078 -0.052013 -0.002040 0.006368 -0.016896 0.026865 -0.053476 -0.043654 -0.016720 0.067789 -0.027404 0.011298 0.029721 0.047551 -0.004781 -0.013614 -0.015427 -0.005603 -0.012131 -0.022415 -0.004610 0.001564 0.077873 0.089689 -0.019509 -0.005804 -0.078648 -0.031269 0.055601 -0.009002 0.005704 0.047165 0.053376 0.055967 0.051981 0.060595 0.028805 0.013425 0.045479 0.030319 0.053645 0.035367 -0.022763 -0.001068 0.019946 0.006964 -0.006634 0.006811 -0.028253 0.026889 0.030947 0.024699 -0.005305 -0.013617 -0.006680 -0.021192 -0.004802 0.081761 0.091831 -0.015784 -0.003912 0.039663 0.034720 0.048705 0.034514 0.039585 0.006829 0.029948 0.034594 0.049724 0.030853 -0.023049 -0.002490 -0.002465 -0.004971 0.029402 0.019723 -0.006805 0.008378 -0.006379 -0.019362 -0.042632 -0.030177 0.014251 -0.005196 0.047902 -0.022858 0.013846 -0.026333 0.000275 0.109569 0.120304 0.004431 0.047553 0.111609 0.108573 0.106426 0.015519 -0.020213 -0.007446 0.000862 -0.008346 0.060587 0.036375 -0.055426 0.038237 0.059643 0.001219 0.009500 0.014789 0.028547 0.056174 -0.006763 -0.011571 -0.009226 -0.023892 -0.043752 -0.030856 0.025411 -0.011565 -0.046372 0.019338 -0.006711 0.035182 -0.003532 -0.006456 0.025188 -0.030051 0.014634 0.131587 0.054925 0.057574 0.007691 0.036722 0.013677 -0.010401 -0.005837 0.011283 0.043849 0.008555 0.049021 0.022330 0.026177 -0.043051 0.045828 -0.001656 -0.032233 -0.034713 -0.028488 -0.049633 -0.013601 0.005034 -0.002653 1.000000
In [23]:
#Visualize the above correlation using heat map
plt.figure(figsize = (20,18))
sns.heatmap(Data.corr(), annot = True)
Out[23]:
<matplotlib.axes._subplots.AxesSubplot at 0x1ecc5b543a0>
In [24]:
# Since highly correlated columns can help building the model in same way, we can drop on of the two highly corelated column 
corr_matrix = Data.corr()
iters = range(len(corr_matrix.columns) - 1)
drop_cols = []

 # Iterate through the correlation matrix and compare correlations
for i in iters:
    for j in range(i-1):
        if i != 0:
            item = abs(corr_matrix.iloc[i, j])
            col = corr_matrix.columns[i]
            row = corr_matrix.index[j]
            # If correlation exceeds the threshold
            if item >= 0.90:
                # Print the correlated features and the correlation value
                print('Columns', col,'and column', row, 'are highly correlated with',item,'ratio')
                drop_cols.append(col)

print ('\nColumns with high correlations which can be dropped are:\n', np.unique(drop_cols))
                
Columns 50 and column 46 are highly correlated with 0.9044818259166801 ratio
Columns 70 and column 66 are highly correlated with 0.9044609903388564 ratio
Columns 140 and column 4 are highly correlated with 0.9999751247610721 ratio
Columns 152 and column 148 are highly correlated with 0.9910694582650661 ratio
Columns 154 and column 148 are highly correlated with 0.9396050560127642 ratio
Columns 199 and column 196 are highly correlated with 0.9419809272931734 ratio
Columns 204 and column 67 are highly correlated with 0.9022307064188807 ratio
Columns 207 and column 196 are highly correlated with 0.9167918615124543 ratio
Columns 252 and column 117 are highly correlated with 0.9861933657838743 ratio
Columns 270 and column 135 are highly correlated with 0.9464739349956607 ratio
Columns 271 and column 136 are highly correlated with 0.9712649283173527 ratio
Columns 272 and column 137 are highly correlated with 0.9768378109004264 ratio
Columns 273 and column 138 are highly correlated with 0.9191717004943438 ratio
Columns 274 and column 139 are highly correlated with 0.985728144360803 ratio
Columns 275 and column 4 are highly correlated with 0.9999755698304483 ratio
Columns 275 and column 140 are highly correlated with 0.9999999763805127 ratio
Columns 283 and column 148 are highly correlated with 0.9995218286822887 ratio
Columns 283 and column 152 are highly correlated with 0.9917748644859977 ratio
Columns 283 and column 154 are highly correlated with 0.9362410275128739 ratio
Columns 286 and column 151 are highly correlated with 0.9900031988390751 ratio
Columns 287 and column 148 are highly correlated with 0.9910771233820856 ratio
Columns 287 and column 152 are highly correlated with 0.9999970976317996 ratio
Columns 287 and column 283 are highly correlated with 0.9917862663223181 ratio
Columns 294 and column 159 are highly correlated with 0.9932395425046503 ratio
Columns 295 and column 160 are highly correlated with 0.9964804116578476 ratio
Columns 296 and column 161 are highly correlated with 0.9946485928894574 ratio
Columns 297 and column 162 are highly correlated with 0.9884014877258684 ratio
Columns 324 and column 188 are highly correlated with 0.97530226992646 ratio
Columns 332 and column 196 are highly correlated with 0.9638588005990898 ratio
Columns 332 and column 197 are highly correlated with 0.9050712800485732 ratio
Columns 332 and column 199 are highly correlated with 0.90309501091955 ratio
Columns 332 and column 207 are highly correlated with 0.9145387691147532 ratio
Columns 333 and column 197 are highly correlated with 0.9825963154934192 ratio
Columns 335 and column 196 are highly correlated with 0.9310646142679881 ratio
Columns 335 and column 199 are highly correlated with 0.963222869738428 ratio
Columns 335 and column 332 are highly correlated with 0.9614071701136431 ratio
Columns 336 and column 196 are highly correlated with 0.9114108834493966 ratio
Columns 336 and column 207 are highly correlated with 0.9014946530204482 ratio
Columns 336 and column 332 are highly correlated with 0.9416465043771408 ratio
Columns 336 and column 333 are highly correlated with 0.9019285474205442 ratio
Columns 338 and column 202 are highly correlated with 0.9910117969269783 ratio
Columns 339 and column 203 are highly correlated with 0.9827091137191302 ratio
Columns 340 and column 67 are highly correlated with 0.9466368752862829 ratio
Columns 340 and column 204 are highly correlated with 0.9853734316133732 ratio
Columns 341 and column 67 are highly correlated with 0.9053174973585882 ratio
Columns 341 and column 205 are highly correlated with 0.991697006650239 ratio
Columns 343 and column 196 are highly correlated with 0.9009438618357838 ratio
Columns 343 and column 207 are highly correlated with 0.9847308409275753 ratio
Columns 343 and column 332 are highly correlated with 0.9355397199453718 ratio
Columns 343 and column 335 are highly correlated with 0.9182601200118453 ratio
Columns 343 and column 336 are highly correlated with 0.9196307731648184 ratio
Columns 344 and column 208 are highly correlated with 0.9636875346683662 ratio
Columns 361 and column 223 are highly correlated with 0.9788025881044046 ratio
Columns 363 and column 225 are highly correlated with 0.9634701123157058 ratio
Columns 388 and column 250 are highly correlated with 0.9746150086226977 ratio
Columns 390 and column 117 are highly correlated with 0.9862339054518461 ratio
Columns 390 and column 252 are highly correlated with 0.9999914227740386 ratio
Columns 413 and column 4 are highly correlated with 0.9384157839693659 ratio
Columns 413 and column 140 are highly correlated with 0.9380778546861439 ratio
Columns 413 and column 275 are highly correlated with 0.938091794288112 ratio
Columns 415 and column 142 are highly correlated with 0.9926143870057542 ratio
Columns 421 and column 148 are highly correlated with 0.9988153783986575 ratio
Columns 421 and column 152 are highly correlated with 0.9835906743060074 ratio
Columns 421 and column 154 are highly correlated with 0.9543904536236193 ratio
Columns 421 and column 283 are highly correlated with 0.9978742631844328 ratio
Columns 421 and column 287 are highly correlated with 0.9835961853911365 ratio
Columns 424 and column 151 are highly correlated with 0.9762310553985684 ratio
Columns 424 and column 286 are highly correlated with 0.9669621166080141 ratio
Columns 425 and column 148 are highly correlated with 0.9618511427358277 ratio
Columns 425 and column 152 are highly correlated with 0.9750918692373749 ratio
Columns 425 and column 283 are highly correlated with 0.962216547566731 ratio
Columns 425 and column 287 are highly correlated with 0.9749103402648396 ratio
Columns 425 and column 421 are highly correlated with 0.95460076984744 ratio
Columns 434 and column 430 are highly correlated with 0.948040387326675 ratio
Columns 434 and column 431 are highly correlated with 0.933359481656668 ratio
Columns 435 and column 430 are highly correlated with 0.9516726155512237 ratio
Columns 435 and column 431 are highly correlated with 0.9295443808853142 ratio
Columns 436 and column 430 are highly correlated with 0.9537232380401666 ratio
Columns 436 and column 431 are highly correlated with 0.9325979460533955 ratio
Columns 436 and column 434 are highly correlated with 0.9923330260757832 ratio
Columns 457 and column 185 are highly correlated with 0.9967773319711016 ratio
Columns 471 and column 199 are highly correlated with 0.9382814829148212 ratio
Columns 477 and column 67 are highly correlated with 0.9218150346605667 ratio
Columns 477 and column 205 are highly correlated with 0.9866216754851614 ratio
Columns 477 and column 332 are highly correlated with 0.9062085846699987 ratio
Columns 477 and column 341 are highly correlated with 0.9882192885279739 ratio
Columns 495 and column 223 are highly correlated with 0.9966769257758836 ratio
Columns 495 and column 361 are highly correlated with 0.9748289745381955 ratio
Columns 497 and column 225 are highly correlated with 0.9930712184247211 ratio
Columns 497 and column 363 are highly correlated with 0.9611210453127839 ratio
Columns 522 and column 250 are highly correlated with 0.985970805836949 ratio
Columns 522 and column 388 are highly correlated with 0.9640282170040964 ratio
Columns 524 and column 117 are highly correlated with 0.9786433214466849 ratio
Columns 524 and column 252 are highly correlated with 0.9958043409065614 ratio
Columns 524 and column 390 are highly correlated with 0.9956676752306468 ratio
Columns 576 and column 572 are highly correlated with 0.994772146241892 ratio

Columns with high correlations which can be dropped are:
 ['140' '152' '154' '199' '204' '207' '252' '270' '271' '272' '273' '274'
 '275' '283' '286' '287' '294' '295' '296' '297' '324' '332' '333' '335'
 '336' '338' '339' '340' '341' '343' '344' '361' '363' '388' '390' '413'
 '415' '421' '424' '425' '434' '435' '436' '457' '471' '477' '495' '497'
 '50' '522' '524' '576' '70']
In [25]:
print ('As per above correlation calculation, we can further drop', len(np.unique(drop_cols)), 'number of features')
drop_cols_temp = np.unique(drop_cols)
drop_cols_temp
As per above correlation calculation, we can further drop 53 number of features
Out[25]:
array(['140', '152', '154', '199', '204', '207', '252', '270', '271',
       '272', '273', '274', '275', '283', '286', '287', '294', '295',
       '296', '297', '324', '332', '333', '335', '336', '338', '339',
       '340', '341', '343', '344', '361', '363', '388', '390', '413',
       '415', '421', '424', '425', '434', '435', '436', '457', '471',
       '477', '495', '497', '50', '522', '524', '576', '70'], dtype='<U3')
In [26]:
print ('shape of the Data set before dropping highly correlated features is', Data.shape)
for i in drop_cols_temp:
    del Data[i]

print ('shape of the Data set after dropping highly correlated features is', Data.shape)
shape of the Data set before dropping highly correlated features is (1567, 183)
shape of the Data set after dropping highly correlated features is (1567, 130)
In [27]:
new_corr_matrix = Data.corr()
new_corr_matrix.tail(1)
#From below, we can see that out of all the columns, column number  21,59, 430,431, 510 has a little better correlation with Pass/Fal column
Out[27]:
0 1 2 3 4 6 12 15 21 22 23 24 28 40 43 45 46 48 51 55 59 60 62 63 64 65 66 67 68 71 72 73 88 90 115 117 133 135 136 137 138 139 142 148 150 151 159 160 161 162 180 182 183 185 187 188 196 197 200 201 202 203 205 208 223 225 250 268 345 346 412 417 418 419 423 428 429 430 431 432 433 438 439 440 456 460 467 468 470 472 473 474 476 478 480 482 483 484 485 486 487 488 489 490 494 496 499 500 510 511 519 520 521 523 525 547 548 550 555 561 562 569 570 572 574 577 581 585 589 Pass/Fail
Pass/Fail -0.025141 -0.002603 -0.000957 -0.024623 -0.013756 0.016239 -0.005969 -0.002884 0.107997 -0.07338 0.012873 -0.018297 -0.106767 -0.051763 -0.02047 0.008347 -0.009413 -0.015267 0.006005 -0.008948 0.155771 -0.018342 -0.019012 0.059912 0.076551 0.054817 -0.039026 0.039532 -0.052078 -0.00204 0.006368 -0.016896 0.026865 -0.053476 -0.043654 -0.01672 0.067789 -0.027404 0.011298 0.029721 0.047551 -0.004781 -0.015427 -0.005603 -0.012131 -0.022415 0.077873 0.089689 -0.019509 -0.005804 -0.078648 -0.031269 0.055601 -0.009002 0.005704 0.047165 0.053376 0.055967 0.060595 0.028805 0.013425 0.045479 0.053645 -0.022763 -0.001068 0.019946 0.006964 0.006811 -0.00249 -0.002465 0.008378 -0.042632 -0.030177 0.014251 0.047902 -0.026333 0.000275 0.109569 0.120304 0.004431 0.047553 0.015519 -0.020213 -0.007446 0.000862 0.060587 0.036375 -0.055426 0.038237 0.001219 0.0095 0.014789 0.028547 -0.006763 -0.011571 -0.009226 -0.023892 -0.043752 -0.030856 0.025411 -0.011565 -0.046372 0.019338 -0.006711 0.035182 -0.006456 -0.030051 0.014634 0.131587 0.054925 0.057574 0.007691 0.036722 -0.010401 0.011283 0.043849 0.008555 0.049021 0.02233 0.026177 -0.043051 0.045828 -0.001656 -0.032233 -0.034713 -0.049633 -0.013601 0.005034 -0.002653 1.0
In [28]:
#Lets see bivariate analysis for above column with respect to Pass/Fail column
sns.lmplot(x='21',y='59',data = Data, hue = 'Pass/Fail')
# we can see the distribution of the pass and fail conductors is situated on extreme negative values of feature 21
Out[28]:
<seaborn.axisgrid.FacetGrid at 0x1ecc2662fa0>
In [29]:
sns.lmplot(x='430',y='431',data = Data, hue = 'Pass/Fail')
#We can see a positive slope between 430 and 431 and distribution is mostly concentrated new 0
Out[29]:
<seaborn.axisgrid.FacetGrid at 0x1ecd8c75670>
In [30]:
sns.lmplot(x='510',y='431',data = Data, hue = 'Pass/Fail')
# we can see that there are many outliers for feaure 510  
Out[30]:
<seaborn.axisgrid.FacetGrid at 0x1ecc6cb37c0>
In [31]:
#Lets check the value counts for each Pass/Fail condutors
Data['Pass/Fail'].value_counts()
# we can see that data is highly imbalance, so we can try balancing it and then creating the models on same
Out[31]:
-1    1463
 1     104
Name: Pass/Fail, dtype: int64
In [32]:
# now that we have cleaned the data and visualized it, lets devide the data into training and testing samples
x = Data.drop(columns = ['Pass/Fail'])
y = Data['Pass/Fail']
x.shape , y.shape
Out[32]:
((1567, 129), (1567,))
In [33]:
#Split into taining and testing data
X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.30, random_state=1)
X_train.shape, X_test.shape, y_train.shape, y_test.shape
Out[33]:
((1096, 129), (471, 129), (1096,), (471,))
In [34]:
from imblearn.over_sampling import SMOTE

print("Before Upsampling, counts of label '-1': {}".format(sum(y_train==-1)))
print("Before Upsampling, counts of label '1': {} \n".format(sum(y_train==1)))

sm = SMOTE(k_neighbors = 5, random_state=1)   #Synthetic Minority Over Sampling Technique
X_train_res, y_train_res = sm.fit_sample(X_train, y_train.ravel())


print("After Upsampling, counts of label '-1': {}".format(sum(y_train_res==-1)))
print("After Upsampling, counts of label '1': {} \n".format(sum(y_train_res==1)))



print('After Upsampling, the shape of X_train_X: {}'.format(X_train_res.shape))
print('After Upsampling, the shape of Y_train: {} \n'.format(y_train_res.shape))
Before Upsampling, counts of label '-1': 1024
Before Upsampling, counts of label '1': 72 

After Upsampling, counts of label '-1': 1024
After Upsampling, counts of label '1': 1024 

After Upsampling, the shape of X_train_X: (2048, 129)
After Upsampling, the shape of Y_train: (2048,) 

In [35]:
# Lets build the lgistic model for above
from sklearn.linear_model import LogisticRegression

LR_model = LogisticRegression()
LR_model.fit(X_train_res,y_train_res)

# Prediction on of test data
y_pred = LR_model.predict(X_test)
LR_model_score = LR_model.score(X_test, y_test)

# Let's measure the accuracy of this model's prediction
print('Accuracy of the Logistic regression model on Original data is', LR_model_score*100)
#We can see that models performance is increased due to scaled values
print('\n\n Classification Report:')
print(metrics.classification_report(y_test, y_pred))
Accuracy of the Logistic regression model on Original data is 69.00212314225053


 Classification Report:
              precision    recall  f1-score   support

          -1       0.93      0.72      0.81       439
           1       0.07      0.28      0.11        32

    accuracy                           0.69       471
   macro avg       0.50      0.50      0.46       471
weighted avg       0.87      0.69      0.76       471

In [36]:
# Plotting confusion matrix
plot_confusion_matrix(LR_model,X_test,y_test)
Out[36]:
<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay at 0x1ecd95b6130>

Explanation of Classification report:

Recall:
Model predicted 316 cases correctly as semicondutor are passed while predicted 123 to be fail where as they were actually pass(this is Recall)
Model predicted 23 cases incorrectly as semicondutor are pass where as they were fail and predicted 9 to be fail which are actually fail (this is Recall)

Precision:
We can see that our model's precision in predicting Pass(-1) is 93% as it has rightly predicted 316 condutors as Pass out of (316+23) total number of pass conductors and model's precision in predicting Fail(1) is 7% as it has incorrectly predicted 123 condutors as Fail out of (123+9) total number of Fail conductors

F1 score is the middle way / average of both Precision and Recall: Hence our model's F1-score for Pass conductors is 81% and for Fail conductors is 11%

And lastly, Model's overall accuracy is 69%

In [37]:
# Lets  implement K fold cross validation
from sklearn.model_selection import KFold
from sklearn.model_selection import cross_val_score

kfold = KFold(n_splits=10, random_state=1)
model = LogisticRegression()
KFCV_results = cross_val_score(model, X_train_res, y_train_res, cv=kfold)
print('Accuracy for 10 folds is',KFCV_results)
print(" Overall Accuracy and its standard deviation is: %.3f%% (%.3f%%)" % (KFCV_results.mean()*100.0, KFCV_results.std()*100.0))
Accuracy for 10 folds is [0.70731707 0.67317073 0.60487805 0.66829268 0.72195122 0.71707317
 0.74634146 0.76585366 0.70098039 0.76470588]
 Overall Accuracy and its standard deviation is: 70.706% (4.666%)
In [38]:
#WE can assume that this after applying k fold cross validation our model is likely
# to perform with the accuracy of between 66% to 74 % in production
In [39]:
# Lets implement LeaveoneOut cross validation
from sklearn.model_selection import LeaveOneOut

LOOCV_results = cross_val_score(model, X_train_res, y_train_res, cv=LeaveOneOut())
print('Accuracy for leave one out CV is',LOOCV_results)
print(" Overall Accuracy and its standard deviation is: %.3f%% (%.3f%%)" % (LOOCV_results.mean()*100.0, LOOCV_results.std()*100.0))
Accuracy for leave one out CV is [1. 1. 1. ... 0. 1. 1.]
 Overall Accuracy and its standard deviation is: 76.074% (42.663%)
In [40]:
# Lets implement StratifiedKFold cross validation

from sklearn.model_selection  import StratifiedKFold
stratified_kfold_CV = StratifiedKFold(n_splits = 10, random_state = 1)
StatifiedKF_results = cross_val_score(model, X_train_res, y_train_res, cv = stratified_kfold_CV)
print('Accuracy for stratified kfold CV is',StatifiedKF_results)
print(" Overall Accuracy and its standard deviation is: %.3f%% (%.3f%%)" % (StatifiedKF_results.mean()*100.0, StatifiedKF_results.std()*100.0))
Accuracy for stratified kfold CV is [0.70731707 0.71707317 0.78536585 0.77073171 0.75121951 0.77560976
 0.74634146 0.7902439  0.7745098  0.76960784]
 Overall Accuracy and its standard deviation is: 75.880% (2.662%)

We can see that the best accuracy which is observed is with leave one out CV, however since it is time and resource consuming, we can consider Stratified k fold CV which is gives average accuracy of around 73% to 77%.

In [41]:
#Lets apply Gridsearch CV to find best hyper parameters
from sklearn.model_selection import GridSearchCV
from sklearn.model_selection import RandomizedSearchCV

LR_GSV = LogisticRegression()

# specify parameters and distributions to sample from
LR_GSV_param = {"penalty" : ['l1', 'l2', 'elasticnet', None],
              "solver" : ['newton-cg', 'lbfgs', 'liblinear', 'sag', 'saga'],
              "dual": [True, False]}

# run randomized search
samples = 10  # number of random samples 
randomCV = RandomizedSearchCV(LR_GSV, param_distributions=LR_GSV_param, n_iter=samples) #default cv = 3
randomCV.fit(X_train_res, y_train_res)
print('Parameters suggested as per random CV', randomCV.best_params_)

# run Grid search
grid_search = GridSearchCV(LR_GSV, param_grid=LR_GSV_param)
grid_search.fit(X_train_res, y_train_res)
print('Parameters suggested as per Grid search CV', grid_search.best_params_)
Parameters suggested as per random CV {'solver': 'sag', 'penalty': 'l2', 'dual': False}
Parameters suggested as per Grid search CV {'dual': False, 'penalty': 'l2', 'solver': 'newton-cg'}
In [42]:
LR_GSV_1 = LogisticRegression(solver ='newton-cg', penalty = 'l2', dual =  False)
LR_GSV_1.fit(X_train_res,y_train_res)

# Prediction on of test data
y_pred = LR_GSV_1.predict(X_test)
LR_GSV_1_score = LR_GSV_1.score(X_test, y_test)

# Let's measure the accuracy of this model's prediction
print('Accuracy of the Logistic regression model on Original data is', LR_GSV_1_score*100)
#We can see that models performance is increased due to scaled values
print('\n\n Classification Report:')
print(metrics.classification_report(y_test, y_pred))
# Plotting confusion matrix
print ('Confusion matrix')
plot_confusion_matrix(LR_GSV_1,X_test,y_test)
Accuracy of the Logistic regression model on Original data is 80.89171974522293


 Classification Report:
              precision    recall  f1-score   support

          -1       0.94      0.85      0.89       439
           1       0.12      0.28      0.17        32

    accuracy                           0.81       471
   macro avg       0.53      0.56      0.53       471
weighted avg       0.89      0.81      0.84       471

Confusion matrix
Out[42]:
<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay at 0x1ecda3dc670>

For solver ='lbfgs': Models performance is 69.02% and solver ='newton-cg': Models performance is 80.89%
(Note: I have changed the solver value and noted the accuracy with solver ='lbfgs')

In [43]:
#lets try different techniques to get the best results
# standardise the training data by applying zscore
x_sc = x.apply(zscore)
x_sc.head()
Out[43]:
0 1 2 3 4 6 12 15 21 22 23 24 28 40 43 45 46 48 51 55 59 60 62 63 64 65 66 67 68 71 72 73 88 90 115 117 133 135 136 137 138 139 142 148 150 151 159 160 161 162 180 182 183 185 187 188 196 197 200 201 202 203 205 208 223 225 250 268 345 346 412 417 418 419 423 428 429 430 431 432 433 438 439 440 456 460 467 468 470 472 473 474 476 478 480 482 483 484 485 486 487 488 489 490 494 496 499 500 510 511 519 520 521 523 525 547 548 550 555 561 562 569 570 572 574 577 581 585 589
0 0.224309 0.849725 -0.436273 0.033555 -0.050580 -0.563790 0.762960 0.103782 0.318407 0.735468 -0.172210 0.361942 -1.522972 -0.277120 -0.452853 -0.812566 -0.852092 0.277786 1.000167 -0.862453 -0.492923 -0.703759 -0.912878 0.303390 0.238540 0.338549 -1.112014 -0.051474 0.274977 -0.641197 2.202065e-15 -2.756181e-14 -1.124999 -0.399317 0.025089 -0.030126 -0.508797 0.087736 -0.500002 -0.911233 -0.928122 -0.252239 0.039159 0.202177 -0.785516 -0.121545 0.136767 0.716844 -0.708552 -0.676486 0.585204 0.410790 -1.456170 -0.229080 -0.784050 1.020904 -0.210990 0.000692 -0.842151 -0.483037 -0.420311 -0.794544 -0.035615 0.858783 0.949805 2.111519 2.020788 2.915403 1.445095e-16 -7.409720e-17 -0.330741 -0.544682 0.712654 -0.950558 -0.736484 -0.089261 -0.087582 0.009596 0.296967 -0.579100 -0.693900 -0.299206 -0.739976 -1.658054 -0.760944 0.055677 -0.005415 0.379989 -0.519154 -1.557287 -0.654667 -0.967680 0.795451 -0.025367 1.126992 1.057855 0.443864 1.321592 -0.105725 1.896453 -0.914914 -1.197906 -1.203118 -0.174360 0.184098 -0.526473 -0.811180 -0.746780 0.236543 -0.837955 1.524217e-16 -0.124479 -0.112621 -0.083086 -0.622220 -1.725401 0.023303 -0.900504 -0.555732 0.531334 -8.200826e-14 -9.956414e-15 0.190142 -0.226018 -0.226665 -0.135520 5.175234e-16 -0.197113 -1.665950e-15
1 1.107136 -0.382910 1.017137 0.153067 -0.060045 0.198217 0.181365 0.095858 0.282478 -0.322234 0.223050 -0.462653 -0.311560 0.433389 -0.528735 -0.455157 -0.727349 1.298783 0.784225 -0.123389 -0.226438 -0.524040 -0.292963 -0.434592 -0.271798 0.070146 -0.816767 -0.050700 1.638845 -0.695974 2.202065e-15 -2.756181e-14 2.313733 -1.079102 -0.329673 0.006493 -0.910429 -0.347544 -1.076326 -0.799950 -0.114196 -0.751798 -0.266339 0.206199 -0.163470 -0.031341 -0.320415 -0.864326 -0.890126 -0.232181 -0.309186 -0.153925 -1.508133 -0.062045 -1.032759 1.833098 -0.315577 -0.047747 -1.105172 -0.805146 -0.446433 -0.860664 -0.007826 2.177719 0.101235 2.223278 1.527628 1.398051 1.445095e-16 -7.409720e-17 -0.867453 0.214656 -1.114221 0.184261 -0.484365 -0.133261 -0.157359 -0.221601 -0.552599 -0.720873 -0.025415 -0.181118 -0.862419 0.793499 -0.665262 0.844178 -0.174436 1.038832 -0.463083 -1.352250 -0.890206 -0.985241 0.719979 -0.025367 2.452496 -1.142265 0.210182 -1.018301 0.728007 -0.602924 2.221170 -0.632654 -1.203118 0.377697 -0.122839 -0.709929 -0.811180 -0.746780 2.275170 -0.837955 1.524217e-16 -0.187140 -0.112621 -0.093240 -0.624689 1.135963 -0.335951 -0.223469 -0.141962 -0.745572 -8.200826e-14 -9.956414e-15 0.256816 -0.261137 -0.265730 -0.460054 2.007880e+00 0.385059 1.156689e+00
2 -1.114158 0.799102 -0.481289 0.686213 -0.047906 -0.906210 0.633372 0.210561 0.272497 0.008033 -0.174567 -0.557914 -0.684304 -2.242749 1.418662 -0.629808 0.092052 0.246003 0.465399 3.105153 2.194423 1.559140 -0.101633 -0.378507 -0.879523 -0.401058 0.331202 -0.051647 -0.387078 -0.619387 -7.487774e-01 1.393693e+00 -2.278834 1.256492 -0.588677 -0.022382 -0.858902 -0.504244 -0.219277 -0.502556 -1.017646 -0.422569 0.477605 -0.010966 -0.616260 -0.181004 -0.326525 0.405138 -0.781040 -0.411950 -0.372639 0.607839 -0.548787 0.256713 -0.007704 0.778808 -0.229484 -0.032550 -0.100386 -0.539995 0.060919 -0.427553 0.369064 0.226882 1.081806 -0.472988 -0.096130 1.381392 4.562218e-01 8.074462e-01 -0.703292 -0.732677 -1.114221 -0.950558 -0.829909 -0.044628 -0.101012 -0.224990 0.187236 -0.639442 -0.425357 0.155507 0.007099 -0.431880 0.339049 0.237267 -0.372060 -0.881098 0.797420 0.213138 -0.355337 0.319282 -0.452152 -0.025367 0.515421 0.415586 -0.286419 -1.018301 -0.049437 1.558987 -0.631890 -0.643368 -0.097230 -0.953410 0.087593 -0.449449 -0.811180 -0.746780 4.913293 -0.096265 2.160440e+00 0.046768 -0.112621 -0.091359 1.702945 1.641698 -0.331428 -0.188183 -1.078814 -0.396160 6.253138e-01 5.144841e+00 0.257279 -0.199823 -0.188395 -0.590505 -2.744816e-01 0.029833 -1.791486e-01
3 -0.350312 -0.198875 -0.051547 -1.106948 -0.051290 0.503246 0.581223 0.535107 0.239761 -0.173190 -0.513983 -0.468515 -1.898926 0.376833 1.201850 -0.629808 0.016854 0.568516 0.533568 3.105153 2.252754 1.047336 -0.037229 -0.060581 -0.991231 -0.514988 0.322131 -0.051299 0.051274 -1.079763 7.716409e-01 -2.462267e-01 -1.041069 -1.595753 -0.782633 0.005798 -3.619030 0.157381 -0.375442 0.019322 -0.797894 -0.970606 -0.320084 0.256042 0.697634 0.038549 -0.024112 -0.348879 -0.149663 -0.273877 -0.844007 0.934653 -0.600019 -0.233256 0.030648 0.431357 -0.176553 0.333121 -0.466077 -0.376977 0.083064 -0.330209 0.044278 1.131454 0.530337 -0.518068 -0.285006 1.683033 3.613835e-02 -7.384135e-02 -0.712547 -0.131018 -0.008778 -0.950558 0.516013 -0.133629 0.127143 -0.075299 -0.246234 -0.185077 -0.107532 -0.606521 -0.759540 -0.713746 0.170529 -0.113683 -0.372060 -0.868418 1.410003 -0.796330 -0.068257 0.438283 1.026429 -0.025367 2.071671 -0.335060 -0.554443 0.427874 -0.518840 -0.694024 -0.640739 -1.410324 0.285546 1.198057 -0.122128 -0.025267 -0.811180 1.458534 1.534851 -0.837955 -6.528480e-01 -0.044627 -0.112621 -0.085908 0.307254 -6.646047 -1.046058 25.287741 3.225112 1.602627 7.932446e-01 4.223799e-01 0.002548 -0.221613 -0.232808 -0.645708 -4.386698e-01 -0.283417 -2.752459e-01
4 0.242143 0.087526 1.117387 -0.158919 -0.047492 -0.115382 0.610171 0.436445 0.226986 -0.217226 -0.131415 0.143314 -1.927846 0.355468 -0.352913 5.044537 4.610835 -0.416695 1.250334 0.343388 -1.604435 -0.013001 3.196010 1.124845 2.367169 2.395718 3.357220 -0.051464 -0.182947 -1.218682 2.202065e-15 -2.756181e-14 0.384333 0.479681 1.005673 -0.037036 -1.674469 0.018091 0.093053 0.007810 -0.716501 -0.459721 -0.849048 0.307867 0.676632 -0.049782 -0.187028 -0.474258 -0.547757 -0.512296 -1.140123 0.016691 1.618012 -0.471280 0.883699 1.333651 -0.202062 -0.411519 0.250309 -0.455540 -0.118231 0.215744 0.003463 0.679989 -0.973833 0.857771 0.724924 0.048793 1.445095e-16 -7.409720e-17 -0.467901 -0.980861 -1.114221 1.713028 0.232375 -0.072999 -0.046079 -0.157039 -0.319558 -0.440681 -0.911141 -0.861295 -0.865293 0.603609 -0.102354 0.127187 -0.099977 -0.778857 -0.013888 -1.007554 -0.997073 -0.747461 1.512905 -0.025367 1.812519 -0.527226 0.367536 1.166272 0.180080 -1.061192 1.329344 1.582088 -1.203118 0.207997 -0.139003 3.214616 0.092288 -0.746780 2.451234 -0.837955 1.524217e-16 -0.025401 -0.112621 -0.094615 -0.659557 -0.785745 1.123032 0.577065 0.411426 -0.538287 -8.200826e-14 -9.956414e-15 0.085279 -0.227409 -0.222385 -0.454486 5.175234e-16 26.913347 -2.752459e-01

Lets reduce the dimensions using PCA

We can reduce dimensions using PCA by following below steps:

  1. Calculate the covariance matrix.
  2. Calculate the eigenvectors and their eigenvalues.
  3. Sort the eigenvectors according to their eigenvalues in descending order.
  4. Choose the first K eigenvectors (where k is the dimension we'd like to end up with).
  5. Build new dataset with reduced dimensionality. (For this particular module lets try implementing PCA manually, in the next modules we can straight away use PCA.fit_transform funtion to reduce dimensions)
In [44]:
# Calculate the covariance matrix
cov_matrix = np.cov(x_sc.T)
print("cov_matrix shape:",cov_matrix.shape)
print("Covariance_matrix",cov_matrix)
cov_matrix shape: (129, 129)
Covariance_matrix [[ 1.00063857e+00 -1.43931658e-01  4.75868246e-03 ... -1.71312713e-02
   2.36043864e-02  4.17663212e-03]
 [-1.43931658e-01  1.00063857e+00  5.77088798e-03 ...  5.40409063e-02
   2.27405073e-03  4.48254521e-02]
 [ 4.75868246e-03  5.77088798e-03  1.00063857e+00 ... -7.05872633e-03
   1.57621501e-02 -3.29109770e-02]
 ...
 [-1.71312713e-02  5.40409063e-02 -7.05872633e-03 ...  1.00063857e+00
  -4.71262486e-04  5.85661312e-01]
 [ 2.36043864e-02  2.27405073e-03  1.57621501e-02 ... -4.71262486e-04
   1.00063857e+00 -3.80249376e-03]
 [ 4.17663212e-03  4.48254521e-02 -3.29109770e-02 ...  5.85661312e-01
  -3.80249376e-03  1.00063857e+00]]
In [45]:
#Calculating Eigen Vectors & Eigen Values:

eigenvalues, eigenvectors = np.linalg.eig(cov_matrix)
print('Eigen Vectors \n%s', eigenvectors)
print('\n Eigen Values \n%s', eigenvalues)
Eigen Vectors 
%s [[-0.01079434  0.03400482  0.0236541  ...  0.02264396  0.13738896
   0.03971213]
 [ 0.00086035 -0.01157146 -0.04057078 ... -0.19063241  0.19675594
  -0.08778818]
 [-0.007367   -0.00467633 -0.02219941 ...  0.00185485  0.01244536
  -0.00107696]
 ...
 [-0.00658125  0.02272129 -0.05324648 ...  0.01743134  0.08986486
   0.03622402]
 [ 0.00679145  0.00763494 -0.02008637 ... -0.13034193  0.05354158
  -0.05498246]
 [ 0.02523848  0.00175913 -0.04945522 ...  0.02804211  0.05842212
   0.05312988]]

 Eigen Values 
%s [9.49893989e+00 5.23201935e+00 4.64834800e+00 4.18673132e+00
 3.56295506e+00 3.37810472e+00 3.12345870e+00 2.89674025e+00
 2.72000651e+00 2.51900881e+00 2.28411495e+00 2.18189837e+00
 2.02664007e+00 2.00026471e+00 1.91469766e+00 1.83645407e+00
 1.79402083e+00 1.76711618e+00 1.71298676e+00 1.63450091e+00
 1.62291304e+00 1.53812380e+00 1.49349202e+00 1.47674953e+00
 1.43242788e+00 1.41945383e+00 1.37423738e+00 1.35481822e+00
 1.29826108e+00 1.25538723e+00 1.25190102e+00 1.19926256e+00
 1.19093401e+00 1.17007265e+00 1.15445231e+00 1.14611178e+00
 7.03481832e-02 5.94155090e-02 5.19960118e-02 8.08151147e-02
 3.31104019e-02 2.61503845e-02 1.13672967e+00 3.85521310e-02
 3.00886270e-02 1.84406380e-02 9.52933592e-02 1.40946935e-02
 1.10152905e-02 1.36160982e-03 1.55641540e-03 2.33481595e-03
 6.84030772e-03 3.51769377e-03 1.15027072e-01 1.17828022e-01
 1.26178577e-01 4.88641982e-03 4.17592697e-03 1.44688904e-01
 1.63469669e-01 1.10585649e+00 1.10055425e+00 1.55510403e-01
 1.90579638e-01 1.08439546e+00 1.07150209e+00 1.98992777e-01
 2.04952777e-01 2.17683163e-01 2.38167112e-01 1.04974106e+00
 2.54600983e-01 2.67590125e-01 3.32886077e-01 3.53986344e-01
 1.03718238e+00 3.10791061e-01 3.11860247e-01 1.01219777e+00
 3.73243205e-01 3.97982247e-01 3.02732135e-01 4.12843785e-01
 4.31699740e-01 4.43430161e-01 5.31305846e-01 4.52064251e-01
 2.85354533e-01 5.05880867e-01 5.18539264e-01 5.60532457e-01
 5.77507549e-01 4.88154781e-01 1.00452245e+00 6.19578310e-01
 4.80912499e-01 4.70548386e-01 9.95808246e-01 6.38414545e-01
 6.31251028e-01 9.76647103e-01 6.69512273e-01 6.75743546e-01
 2.82148562e-01 9.63869054e-01 7.02580147e-01 7.14764394e-01
 9.53139311e-01 9.44533513e-01 9.56803478e-01 7.30332879e-01
 9.27678718e-01 7.46779805e-01 7.76660204e-01 7.80506671e-01
 8.84814936e-01 8.94329204e-01 9.05194588e-01 8.45432166e-01
 9.04127955e-01 8.33806830e-01 8.60588941e-01 8.17227089e-01
 7.66834865e-01 8.21746586e-01 8.65501139e-01 8.02081294e-01
 8.02132841e-01]
In [46]:
#Sort eigenvalues in descending order

# Make a set of (eigenvalue, eigenvector) pairs:
eig_pairs = [(eigenvalues[i], eigenvectors[:,i]) for i in range(len(eigenvalues))]

# Sort the (eigenvalue, eigenvector) pairs from highest to lowest with respect to eigenvalue
eig_pairs.sort()

eig_pairs.reverse()
print(eig_pairs)

# Extract the descending ordered eigenvalues and eigenvectors
eigvalues_sorted = [eig_pairs[index][0] for index in range(len(eigenvalues))]
eigvectors_sorted = [eig_pairs[index][1] for index in range(len(eigenvalues))]

# Let's confirm our sorting worked, print out eigenvalues
print('Eigenvalues in descending order: \n%s' %eigvalues_sorted)
[(9.498939889577516, array([-1.07943385e-02,  8.60347823e-04, -7.36699964e-03, -8.67263362e-05,
        2.32333249e-03,  6.09987282e-03, -7.29962812e-03,  2.65589280e-02,
       -1.04009577e-02,  9.74364760e-03, -1.13800972e-02,  3.18999152e-03,
       -4.67133877e-04, -5.12040213e-03,  1.95403670e-02,  4.78906416e-02,
        5.37694841e-02, -1.37714779e-02,  2.09272951e-02,  1.15956203e-02,
        1.29666014e-01, -1.88266088e-02,  1.82670423e-01,  1.71921261e-01,
        4.63501681e-02,  1.11416946e-01,  3.19245835e-02,  2.67406421e-01,
       -1.35291133e-01, -2.06200355e-02, -7.63062129e-02,  1.42007304e-01,
       -4.90055702e-03, -6.78387430e-03,  1.93576464e-03, -2.79738631e-03,
       -2.32613986e-02,  5.13119293e-03, -2.05609629e-02, -2.79152016e-02,
       -1.53163061e-02,  9.14320625e-05,  3.18520868e-03,  1.64434698e-03,
       -4.69129433e-03,  6.66116574e-02, -1.21115536e-02, -9.96200336e-03,
       -4.73455990e-03, -9.65299957e-03,  8.04504124e-03,  5.77981174e-02,
        2.15502051e-02,  6.53289721e-03,  1.23016733e-02,  1.27811386e-02,
        3.02870644e-01,  2.82157033e-01,  2.21847179e-01,  1.87114386e-01,
        2.49544663e-01,  2.73945556e-01,  2.80691928e-01,  3.25371193e-02,
       -5.91253281e-03, -3.65616414e-03, -3.94444145e-03,  2.33162937e-02,
        2.25848113e-01,  2.19446040e-01, -5.55710566e-04,  1.12221522e-02,
        2.01210180e-03,  5.15064937e-03, -1.65706296e-02, -7.18886889e-03,
        2.76667889e-03, -1.17359952e-02, -1.11301897e-02, -4.83874557e-03,
       -4.44411182e-03,  1.02492935e-03, -1.31203589e-03,  2.21078435e-03,
        6.22158593e-03, -1.08572214e-02, -1.58746919e-02,  1.45436102e-02,
        2.42302105e-01,  6.19574362e-02,  1.36711042e-01,  2.23079175e-01,
        1.61719093e-01,  1.46770947e-01,  4.64640548e-02,  4.31831365e-03,
       -1.38280028e-02,  1.32301848e-02,  9.41574685e-03,  5.56070386e-03,
       -6.68976684e-03, -1.05485361e-02,  3.79870937e-03, -3.23701685e-03,
       -7.53302721e-04,  9.40043253e-03, -1.98350672e-03, -1.73956206e-02,
        8.58873857e-03,  2.01289235e-02,  3.71450862e-04,  3.80476390e-03,
        3.90815221e-03,  9.93383696e-02,  4.01607382e-03,  9.87485638e-03,
       -6.43990155e-03,  6.82346856e-03,  1.89083390e-03,  1.25276830e-02,
        4.63236696e-03, -5.32375881e-03, -2.91895174e-02,  1.71232166e-02,
        1.58216709e-02,  2.24714437e-02, -6.58124830e-03,  6.79145008e-03,
        2.52384796e-02])), (5.232019349425661, array([ 0.03400482, -0.01157146, -0.00467633,  0.05931959,  0.03305899,
       -0.0805247 , -0.02430123,  0.0209576 , -0.03815494, -0.00839459,
       -0.04090692, -0.03468872,  0.21350587,  0.07177561,  0.07156617,
        0.17930591,  0.20342349, -0.10864959, -0.03632154,  0.03602914,
       -0.18536674,  0.13545414,  0.12594814, -0.1449385 , -0.01883402,
       -0.01136116,  0.20791644, -0.07295002, -0.00359178,  0.14599646,
        0.18980579, -0.11234172, -0.01850713,  0.02298901,  0.02311696,
        0.00098603, -0.05561688, -0.00029914, -0.01384135, -0.01457004,
       -0.06963063,  0.13383619,  0.05859699, -0.00832776, -0.03188527,
        0.03488931, -0.14132037, -0.16982842, -0.01504635,  0.07845243,
        0.1714021 ,  0.15599753, -0.08112663,  0.02147642,  0.00763725,
       -0.03136294,  0.00518844, -0.01196689,  0.00022649,  0.17552975,
        0.09863858,  0.00412505, -0.07947627, -0.11664542,  0.02213983,
        0.00204421,  0.02795438,  0.02440011, -0.1123866 , -0.11046142,
        0.09629159,  0.11765348,  0.03278919,  0.00056938, -0.05094057,
        0.00797451,  0.01170791, -0.1613634 , -0.1825638 , -0.01484086,
        0.07076047,  0.10073454,  0.09736335,  0.18505881,  0.0601103 ,
       -0.00329295, -0.06850152,  0.12047434,  0.04165818,  0.10037699,
        0.18251632,  0.14520239, -0.12000252,  0.07133046, -0.18207174,
       -0.0146373 ,  0.03742955, -0.05804468,  0.03178691, -0.02623281,
        0.08696057, -0.03772741,  0.00496638, -0.03738717, -0.01446387,
        0.02597043,  0.01599927, -0.00504232, -0.12920977,  0.00484367,
       -0.06855322, -0.01240569,  0.00098322, -0.05027547, -0.01154844,
       -0.09245932, -0.16472554, -0.06042151, -0.10084265,  0.00039991,
        0.07289867,  0.0070534 ,  0.08184918, -0.00919754, -0.01095676,
        0.0064606 ,  0.02272129,  0.00763494,  0.00175913])), (4.648347996984388, array([ 2.36540952e-02, -4.05707789e-02, -2.21994112e-02,  2.90780940e-02,
       -2.24080262e-02, -9.79868947e-03,  3.71155259e-02, -6.17854313e-03,
       -3.10998464e-01,  2.83171758e-01, -8.73316591e-02,  4.31350679e-02,
        6.02496340e-02,  3.86783233e-02, -1.44736574e-01, -1.11250913e-01,
       -1.86696669e-01,  1.58969431e-02, -9.11755665e-02, -1.84946912e-01,
        3.77694983e-02, -1.49889003e-01,  7.15264132e-03, -1.00382306e-01,
       -1.69518098e-01, -1.62529813e-01, -8.79246700e-02,  1.30169366e-02,
        6.91342755e-03, -4.88339762e-02, -1.02124495e-01,  8.78431001e-02,
        1.72067201e-02, -1.42853897e-02, -1.61399396e-02,  3.00502543e-03,
        5.03630041e-02,  3.58768346e-02, -3.13978284e-02, -2.51765990e-02,
       -2.55215398e-02, -6.18697333e-02, -5.54373558e-02,  1.98491252e-02,
       -4.38311611e-02, -4.79577864e-03, -3.19406891e-01, -2.34565729e-01,
        3.46705799e-03, -7.42931909e-03,  3.05589074e-02, -1.75290498e-02,
        1.61551246e-01,  6.92510110e-02,  1.05678370e-01, -4.39067476e-02,
       -1.72632217e-02, -1.10399144e-02,  7.62989405e-04, -7.48761124e-02,
       -5.53068824e-02,  3.38611720e-02,  9.76519228e-03,  4.78289798e-02,
        1.16223294e-02, -1.47128463e-02, -2.96562351e-02, -2.17060813e-02,
        7.59644620e-02,  6.91580975e-02, -8.23252438e-02, -1.18704521e-02,
       -1.72510064e-03, -5.56049259e-03, -4.42105345e-02, -9.70655906e-03,
        6.79166566e-03, -3.54896413e-01, -3.28798159e-01, -6.51605324e-02,
       -8.99580085e-02, -1.52216388e-02, -1.54584181e-02, -3.50822620e-02,
        4.34793062e-02,  6.04807266e-02, -7.74389589e-03,  2.10209001e-02,
       -4.44260113e-02,  1.33018784e-01, -9.27998982e-03, -1.17147771e-02,
        4.23527843e-02, -3.50453341e-02,  6.62630511e-02,  1.40272621e-02,
        4.79806579e-03,  5.57699933e-02, -2.15934138e-02,  1.21342789e-02,
       -9.25199296e-03,  2.11717205e-02,  1.85658693e-02,  2.28597907e-02,
        7.51069341e-03, -3.61683768e-02, -1.23647557e-02,  1.49521367e-02,
       -7.15532453e-02,  8.23108533e-05, -4.93092755e-02, -3.45136478e-02,
       -3.79753727e-02,  1.76177557e-02, -9.76764876e-02,  4.49285521e-03,
        1.09255883e-02, -3.55404653e-02,  2.45089374e-02,  5.80672786e-03,
       -2.74308037e-02, -7.37951214e-03, -6.42209566e-02,  1.74848238e-02,
        1.84877911e-02,  9.01176854e-03, -5.32464807e-02, -2.00863749e-02,
       -4.94552216e-02])), (4.186731324975693, array([-2.82939883e-02, -1.41455439e-02,  5.06502121e-03, -7.41554618e-02,
       -1.32463866e-02,  1.06465728e-01,  4.31211187e-02, -3.01814719e-02,
       -1.66531303e-01,  1.31839340e-01, -1.57010111e-02,  5.10263894e-02,
       -1.30871276e-01, -2.70583201e-02,  2.49314693e-01,  2.00091712e-01,
        3.05366963e-01, -1.47229313e-01, -1.21888646e-02,  1.74746759e-01,
        6.77772358e-02,  2.84584155e-01,  2.01019532e-01,  3.56505304e-03,
        7.30789323e-03, -2.57691563e-02,  3.41220307e-01,  2.86710901e-02,
       -1.43577908e-01, -8.12604489e-02,  1.26431710e-01,  1.60320656e-03,
       -2.54946197e-02, -2.38508076e-02, -2.41093116e-02, -8.45062294e-03,
       -5.82622876e-03,  1.97381364e-02, -2.94950448e-02, -1.85219127e-02,
        3.54972188e-04, -1.39248709e-01, -5.92808369e-02,  3.63588397e-02,
       -9.88415969e-03, -9.26516381e-02, -6.74340543e-02, -1.68547456e-02,
       -6.85759942e-03, -1.18708531e-01, -1.19695761e-03,  6.08097739e-02,
       -2.29693977e-02, -8.05431619e-05, -1.58890458e-02, -4.51246065e-02,
       -3.53517374e-02,  1.96188178e-02, -8.14662148e-02, -1.24316037e-01,
       -1.36201739e-01, -1.14205351e-01,  2.52056591e-02,  1.17460347e-01,
       -9.88833252e-03, -6.23739502e-03,  6.63429777e-03,  1.03935950e-01,
       -7.72330992e-04, -1.79452694e-02, -1.09695921e-01, -1.58978893e-02,
       -8.59114445e-03, -1.10411453e-02, -7.08367815e-02, -2.83847339e-03,
       -2.56277000e-03, -7.98422711e-02, -5.83300474e-02, -3.60721700e-02,
       -8.94406396e-02, -1.31493349e-01, -1.26290621e-01, -1.56286820e-01,
        4.24184230e-03, -5.10786541e-02, -7.09802043e-02, -2.92667713e-02,
        7.66088661e-02, -2.19812319e-02, -9.99945406e-02, -8.96911986e-02,
        1.13209924e-01, -1.51951084e-01,  1.63628996e-01,  2.30319271e-03,
       -5.39798027e-02,  6.59112373e-02, -3.80987304e-02, -3.02190684e-02,
       -4.41917743e-02, -2.15553088e-03,  8.22925917e-03,  2.53958334e-02,
        2.08175146e-02,  1.62439494e-02, -1.29125096e-02, -4.75541186e-03,
        5.12080137e-02,  2.85691451e-02,  3.83534162e-03,  1.08613422e-02,
       -1.64877172e-03,  4.16813197e-02, -7.52770306e-03,  5.69015607e-02,
        7.42077138e-02,  4.54616492e-02,  8.39224144e-02,  3.92953397e-03,
        5.76606584e-03, -1.94127892e-02,  3.88739255e-02, -3.04883606e-02,
       -2.92560441e-02, -4.86662018e-02,  3.04873956e-02,  3.70602087e-02,
        2.77419079e-02])), (3.562955057867467, array([ 2.64482899e-02,  1.41606276e-02,  1.07801000e-02,  5.27224635e-02,
       -1.20107009e-04, -5.30039429e-02,  1.40349930e-02, -6.64243293e-02,
        8.36449717e-02, -6.54237773e-02,  2.57201632e-02, -5.56247028e-02,
        9.53373479e-02,  2.71066976e-02,  9.02918947e-02,  2.56410057e-02,
        7.11208985e-02, -3.42663876e-02, -4.20775824e-02,  4.59933279e-02,
       -3.15849937e-02,  7.82936274e-02,  4.02003753e-02,  1.62703144e-02,
        1.83400402e-02, -4.40163851e-02,  1.11026653e-01,  3.31269383e-02,
        3.32942674e-02,  4.48505829e-02, -2.35993528e-01,  2.86768726e-01,
       -3.10111079e-02,  4.16224172e-02,  5.17489167e-02,  1.14258409e-02,
       -4.27144106e-02,  1.52071580e-03, -2.12170232e-02, -3.90870669e-02,
       -1.86502871e-02,  2.73482838e-02, -1.81979810e-02, -2.52843482e-03,
       -4.29938339e-02, -1.01427924e-01,  1.27934068e-02, -1.19360543e-02,
       -1.11494902e-02,  8.72741347e-02,  4.70269687e-02, -1.79851277e-02,
       -7.73244777e-02,  2.65854750e-03, -3.49503967e-02, -5.03570149e-02,
       -3.26332721e-02,  1.96286830e-02, -1.16557991e-01, -1.40841422e-01,
       -1.20067379e-01, -1.10365810e-01,  3.93089941e-03, -1.65325709e-02,
        6.63541244e-03,  1.66512936e-02,  3.01143331e-02, -2.72719881e-02,
        2.24957687e-01,  2.22825330e-01,  6.35660224e-04,  6.77983060e-02,
        2.61929616e-02, -1.86092927e-02, -5.12264568e-02, -8.21558839e-03,
       -1.32305170e-02,  9.70473038e-03, -4.22177460e-03, -7.32373616e-04,
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       -6.62404697e-02,  3.51050366e-01,  5.47066315e-01,  3.48546753e-02,
       -6.08526738e-02,  1.12099010e-03,  6.66540607e-03,  1.48291430e-02,
        3.37543683e-04,  1.62347123e-03, -2.62251676e-03, -5.62684405e-04,
        1.10172697e-03, -3.49570251e-04,  7.08906330e-04, -8.96795238e-04,
       -3.99647629e-04,  1.26462573e-03, -2.70562385e-03, -6.56953321e-04,
        2.08943881e-03,  1.04706511e-03,  2.98688416e-02, -3.46682063e-02,
       -1.91936073e-04,  1.63523298e-03,  1.28597855e-02,  9.82041675e-04,
        1.26295739e-02, -4.61543756e-02, -3.06081191e-02, -1.27836422e-03,
       -3.76256498e-02, -1.61808474e-02, -6.05068379e-02,  4.89838554e-02,
       -3.46463374e-02,  2.03669375e-02,  2.57162257e-02, -1.12785633e-03,
        2.51466959e-04,  7.80223056e-04, -5.57341604e-05,  1.61944051e-03,
        1.52434211e-01, -1.59180340e-01,  1.84687653e-04,  1.09839053e-03,
        7.26214830e-04,  4.63873748e-04,  3.40221006e-04, -8.27891052e-04,
       -8.90856362e-04, -6.31518080e-02,  6.52482616e-02, -1.29615644e-03,
       -6.75227373e-05, -2.74841430e-05,  6.70257405e-04, -1.24124847e-03,
       -2.92171109e-03,  1.85797111e-03, -3.36273172e-03, -2.61497727e-03,
       -2.24098701e-03,  2.93798783e-02, -3.36719647e-02,  1.91829449e-02,
        3.14623502e-03,  3.45786120e-02, -7.27931828e-04, -6.35430303e-04,
       -1.28312716e-04,  7.31993690e-04, -8.69106801e-04,  8.50527813e-04,
       -1.51863249e-03, -1.33467040e-03,  3.60143760e-04, -1.65723226e-03,
       -2.96704217e-04,  1.85794604e-04,  1.38402427e-04,  1.22990527e-03,
        1.49477978e-04, -1.93319497e-03, -1.23651586e-04,  4.74973575e-04,
        1.16819449e-03,  3.19268561e-03, -4.80486731e-04, -1.58178100e-03,
        6.32230104e-04, -5.56047241e-04, -1.37576282e-03, -7.95488586e-05,
       -5.43058197e-04,  5.38527386e-04, -3.97102807e-03,  2.15691582e-02,
       -2.13151810e-02, -2.56966884e-03, -8.72815795e-04,  2.26637114e-04,
        2.07740802e-03]))]
Eigenvalues in descending order: 
[9.498939889577516, 5.232019349425661, 4.648347996984388, 4.186731324975693, 3.562955057867467, 3.3781047188729665, 3.1234586983814996, 2.896740247012644, 2.720006508195297, 2.5190088116427725, 2.284114951260867, 2.1818983656529047, 2.026640067593797, 2.000264711286299, 1.9146976598067214, 1.8364540743240112, 1.794020828040592, 1.7671161813949274, 1.712986756405089, 1.6345009063066522, 1.6229130405662058, 1.5381237972906836, 1.4934920194863357, 1.4767495274172253, 1.4324278819833731, 1.4194538279849158, 1.3742373778836472, 1.3548182238607367, 1.2982610820213651, 1.2553872325196787, 1.2519010183004973, 1.1992625554851697, 1.1909340129758053, 1.1700726461917428, 1.154452314721701, 1.1461117799982323, 1.1367296683503523, 1.1058564927940202, 1.1005542519173042, 1.0843954603265749, 1.071502088995551, 1.0497410645241079, 1.0371823788216288, 1.0121977727831704, 1.0045224476827401, 0.9958082455692998, 0.9766471034002521, 0.9638690538465439, 0.9568034775608198, 0.9531393107346182, 0.9445335130824255, 0.9276787177698929, 0.9051945875625041, 0.9041279547015257, 0.8943292039526343, 0.8848149357993443, 0.8655011392416442, 0.860588941116157, 0.8454321663905576, 0.8338068301443086, 0.82174658607617, 0.8172270891494556, 0.8021328414712544, 0.8020812941732917, 0.7805066711509825, 0.7766602040861745, 0.7668348646315984, 0.7467798045103285, 0.7303328786065549, 0.7147643941394868, 0.702580147277707, 0.6757435455625513, 0.6695122731877595, 0.6384145453387995, 0.6312510279007324, 0.6195783099942663, 0.5775075493400974, 0.5605324571083408, 0.5313058458411763, 0.5185392641516556, 0.5058808666035016, 0.48815478102667087, 0.48091249851444784, 0.4705483856582529, 0.4520642506531529, 0.4434301613462223, 0.4316997399007819, 0.41284378457511933, 0.3979822468322802, 0.3732432045218797, 0.3539863436729204, 0.33288607654119334, 0.3118602467346556, 0.3107910612379128, 0.3027321350599863, 0.2853545325513171, 0.2821485621770654, 0.26759012455768594, 0.254600982853172, 0.2381671122787249, 0.2176831630585945, 0.20495277712210191, 0.19899277700790852, 0.190579637897479, 0.1634696686760357, 0.15551040347596667, 0.14468890444904617, 0.126178577427656, 0.11782802234971994, 0.11502707186036656, 0.09529335923366494, 0.08081511465511029, 0.07034818320620351, 0.05941550900554441, 0.051996011817034324, 0.03855213104402428, 0.033110401949095536, 0.030088627042818113, 0.026150384493922825, 0.01844063797448562, 0.014094693461094172, 0.01101529050517491, 0.006840307724769044, 0.004886419819025011, 0.0041759269748398485, 0.0035176937721913258, 0.0023348159473509968, 0.0015564153983103311, 0.0013616098195192291]
In [47]:
tot = sum(eigenvalues)
var_explained = [(i / tot) for i in eigvalues_sorted]  # an array of variance explained by each 
# eigen vector... there will be 129 entries as there are 129 eigen vectors)
cum_var_exp = np.cumsum(var_explained)  # an array of cumulative variance. There will be 129 entries with 129 th entry 
# cumulative reaching 100%


print('Cumulative Variance explained:\n' , cum_var_exp)
Cumulative Variance explained:
 [0.0735882  0.11412061 0.15013132 0.18256589 0.21016807 0.23633822
 0.26053562 0.28297664 0.30404851 0.32356325 0.34125827 0.35816141
 0.37386177 0.38935781 0.40419095 0.41841795 0.43231621 0.44600604
 0.45927654 0.471939   0.48451169 0.49642752 0.50799759 0.51943796
 0.53053496 0.54153146 0.55217766 0.56267343 0.57273105 0.58245652
 0.59215499 0.60144566 0.61067182 0.61973636 0.62867989 0.63755881
 0.64636504 0.6549321  0.66345809 0.67185889 0.68015981 0.68829214
 0.69632718 0.70416867 0.7119507  0.71966521 0.72723129 0.73469837
 0.74211072 0.74949468 0.75681198 0.7639987  0.77101123 0.7780155
 0.78494386 0.79179851 0.79850354 0.80517052 0.81172007 0.81817957
 0.82454563 0.83087668 0.8370908  0.84330452 0.84935109 0.85536787
 0.86130854 0.86709383 0.87275171 0.87828899 0.88373187 0.88896685
 0.89415355 0.89909935 0.90398964 0.90878951 0.91326346 0.9176059
 0.92172192 0.92573904 0.92965809 0.93343982 0.93716545 0.94081078
 0.94431292 0.94774817 0.95109254 0.95429084 0.957374   0.96026551
 0.96300784 0.96558671 0.96800269 0.97041038 0.97275565 0.97496629
 0.97715209 0.97922511 0.9811975  0.98304258 0.98472897 0.98631673
 0.98785833 0.98933475 0.99060115 0.99180588 0.99292679 0.99390429
 0.9948171  0.99570822 0.99644645 0.99707253 0.99761751 0.99807781
 0.99848062 0.99877928 0.99903579 0.99926888 0.99947147 0.99961433
 0.99972352 0.99980886 0.99986185 0.9998997  0.99993205 0.99995931
 0.99997739 0.99998945 1.        ]
In [48]:
# Plotting the Explained variance and principal components
plt.figure(figsize=(10,5))
plt.bar(range(1,130), var_explained, alpha=0.5, align='center', label='individual explained variance')
plt.step(range(1,130),cum_var_exp, where= 'mid', label='cumulative explained variance')
plt.ylabel('Explained variance ratio')
plt.xlabel('Principal components')
plt.show()

# From below we plot we can not see any particular elbow so lets try selecting number of dimensions based on the cumulative variance explained
# we can see that 75 features explain 90% of the data, so we will use first 75 principal components going forward and calulate the reduced dimensions.
In [49]:
# P_reduce represents reduced mathematical space....

x_reduce = np.array(eigvectors_sorted[0:75])   # Reducing from 129 to 75 dimension space

x_pca = np.dot(x_sc,x_reduce.T)   # projecting original data into principal component dimensions

x_reduced_pca = pd.DataFrame(x_pca)  # converting array to dataframe for pairplot

x_reduced_pca.head()
Out[49]:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74
0 -1.163453 -2.396733 0.163554 0.431128 -0.291643 -1.054599 0.911534 -0.054441 0.196146 0.252531 -0.328450 -0.676090 0.127875 -1.562120 -2.102059 -1.517571 0.521249 -0.886171 -1.267300 -0.278813 -1.618662 0.917258 0.955281 -1.286690 -0.027092 -0.697406 -0.222995 1.404850 -1.150182 -0.037549 -0.356038 0.321769 0.697939 1.714255 0.493094 -0.353475 -0.703971 -0.181684 0.772531 0.318199 0.034142 1.011521 -1.101945 -1.726825 0.896541 0.272611 -0.359435 -0.035249 0.834872 2.013943 -0.701044 -0.102662 0.697089 0.352842 0.038590 0.264686 0.897474 0.713379 -0.197127 -0.824293 -1.100915 -1.135701 0.912250 0.343964 1.176808 0.868350 -0.104809 1.465931 0.562727 -0.485682 -1.254538 -1.329805 -1.137506 0.287792 -1.246909
1 -1.545191 -1.744298 0.432179 0.378855 -0.183718 -1.421468 0.841136 -0.487645 -0.078498 0.349606 -0.895909 0.660900 -1.229965 -0.988639 -3.503881 -0.486649 1.745170 -2.271156 0.148130 -1.292155 0.297530 0.246258 0.353732 1.303990 0.279255 -2.386071 1.365830 -0.865122 -1.248437 -0.876139 -1.141848 -0.665323 0.112224 1.797491 0.657309 -0.569923 1.200862 1.056545 -0.061525 -0.629477 -0.036881 -0.339568 1.372847 -0.260934 -0.338792 -0.183522 0.430305 -0.640051 1.164547 -0.804323 -0.245761 -0.682826 -0.819494 0.608515 0.447998 0.196643 0.343539 -0.894908 -0.397173 1.070460 0.864844 0.592388 0.841974 0.905768 0.854948 2.109583 -0.812823 0.767246 2.532387 0.044418 0.367491 -0.114228 -0.611888 1.142240 -1.019391
2 0.860045 -1.651834 -1.221206 2.390579 0.593729 -1.735366 -0.719669 1.419358 -1.838536 -1.390172 -0.428844 -0.834210 -0.439010 0.714487 -1.261344 0.879023 1.214892 -0.574733 -0.032666 -1.922532 -0.470613 0.672419 -1.926182 1.059461 -0.143582 2.783651 -1.257360 1.053837 0.457986 1.791640 2.586380 0.082402 0.257790 1.653516 1.819283 1.734753 -1.572411 -0.824989 0.964750 -0.173618 -1.692548 0.054716 -0.366977 -1.029313 1.052382 -0.603086 0.909156 -2.641156 -0.267543 1.334477 -1.591412 0.111139 -1.018543 -1.131141 -0.886501 -0.400448 0.867028 -0.120111 -3.325047 -0.810216 0.622516 1.366869 -1.204378 0.227972 -1.102934 1.381201 -0.213805 1.223106 1.696287 0.430952 0.894538 0.066978 -0.277683 0.725075 -0.608610
3 0.882356 -2.788030 -1.610578 4.655940 -2.106891 -3.046918 -1.481106 2.204595 -1.013725 1.142482 -0.711539 0.359093 -0.521430 3.022199 -4.156036 -0.139373 2.416940 1.022970 0.119292 -0.963635 1.609175 0.911552 -1.536609 2.382004 2.289904 0.128736 -0.985622 2.985585 7.071971 4.800494 -3.579417 -4.415538 -3.338633 2.584572 2.992760 -3.359439 7.321620 -1.604284 0.382782 6.859341 -8.374694 -2.556433 -2.034077 0.718443 3.790040 6.091768 0.899226 7.192738 -0.658418 -2.436175 5.199513 4.092708 1.319333 -3.052296 -0.682244 3.110848 -0.042547 5.313440 -3.446089 2.394313 0.649692 -0.301269 3.792983 -3.045137 1.388543 -2.798867 -4.526912 3.008675 -3.131251 3.054224 -2.417240 0.952617 3.307447 -0.547730 0.930823
4 1.645215 0.586966 -2.916893 6.848357 -0.287891 3.910116 4.339091 -4.159801 2.497264 -0.248956 -0.483843 0.720155 2.048752 3.960142 -0.757799 2.215194 1.605159 -3.820181 -3.574692 0.189568 -0.753329 0.762581 0.251675 4.069546 -1.438865 -0.826142 0.519724 -3.458778 -2.259994 -4.179893 -0.028555 -1.880137 -2.119496 6.756367 -1.145346 6.882802 7.321450 0.391154 4.918356 7.431908 -1.824904 7.144568 -0.079447 10.735411 -2.646822 -2.554352 2.262293 2.369519 -2.962687 2.446161 -7.411788 0.536720 2.274107 1.012001 2.876127 -5.577185 -3.735778 -1.741377 -1.905116 3.394340 1.138413 -2.911084 -0.881005 1.078923 4.077711 2.378935 2.317550 -3.084827 -1.722713 -0.184079 -0.596113 1.427634 1.722657 0.156708 -0.395822
In [50]:
#Split into taining and testing data
X_train_sc, X_test_sc, y_train_sc, y_test_sc = train_test_split(x_reduced_pca, y, test_size=0.30, random_state=1)
X_train_sc.shape, X_test_sc.shape, y_train_sc.shape, y_test_sc.shape
Out[50]:
((1096, 75), (471, 75), (1096,), (471,))
In [51]:
# Lets upsample the dataset to balance 
print("Before Upsampling, counts of label '-1': {}".format(sum(y_train_sc==-1)))
print("Before Upsampling, counts of label '1': {} \n".format(sum(y_train_sc==1)))

sm = SMOTE(k_neighbors = 5, random_state=1)   #Synthetic Minority Over Sampling Technique
X_train_sc_res, y_train_sc_res = sm.fit_sample(X_train_sc, y_train_sc.ravel())


print("After Upsampling, counts of label '-1': {}".format(sum(y_train_sc_res==-1)))
print("After Upsampling, counts of label '1': {} \n".format(sum(y_train_sc_res==1)))



print('After Upsampling, the shape of X_train_X: {}'.format(X_train_sc_res.shape))
print('After Upsampling, the shape of Y_train: {} \n'.format(y_train_sc_res.shape))
Before Upsampling, counts of label '-1': 1024
Before Upsampling, counts of label '1': 72 

After Upsampling, counts of label '-1': 1024
After Upsampling, counts of label '1': 1024 

After Upsampling, the shape of X_train_X: (2048, 75)
After Upsampling, the shape of Y_train: (2048,) 

In [52]:
#Lets see if the performance of our model is increased or not


LR_model1 = LogisticRegression()
LR_model1.fit(X_train_sc_res,y_train_sc_res)

# Prediction on of test data
y_pred = LR_model1.predict(X_test_sc)
LR_model1_score = LR_model1.score(X_test_sc, y_test_sc)

# Let's measure the accuracy of this model's prediction
print('Accuracy of the Logistic regression model on Original data is', LR_model1_score*100)
#We can see that models performance is increased due to scaled values
print('\n\n Classification Report:')
print(metrics.classification_report(y_test_sc, y_pred))
print('\n\n Confusion Matrix:')
print(plot_confusion_matrix(LR_model1,X_test_sc,y_test_sc))
Accuracy of the Logistic regression model on Original data is 75.3715498938429


 Classification Report:
              precision    recall  f1-score   support

          -1       0.94      0.78      0.86       439
           1       0.10      0.34      0.16        32

    accuracy                           0.75       471
   macro avg       0.52      0.56      0.51       471
weighted avg       0.89      0.75      0.81       471



 Confusion Matrix:
<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay object at 0x000001ECDA538C40>

Models overall accuracy have increased from 69% to 75% we can see that F1 score is increased by 5% for both -1 and 1 classes of prediction. Also as explained earlier, Precision nd recall for estimating -1 and 1 type of semi conductors have increased.

We can see that by using above techniques we have clearly increased out model's performance

In [53]:
# lets see if the performance of the mode changes when we change the sample population 
# We will create a method which will take independent variables, target variables and 2 ratios 
# based on which we will create 2 samples and run the model on both sample sets and see if the performance is changed 

from sklearn.pipeline import Pipeline 


def diff_sample_test (x,y,sample_ratio1,sample_ratio2):
    print ('shape of X and Y data set before applying enhancement is',x.shape,y.shape,'respectively')
    sm = SMOTE(k_neighbors = 5, random_state=1)   #Synthetic Minority Over Sampling Technique
    xsm,ysm = sm.fit_sample(x, y.ravel())
    
    xtrain1,xtest1,ytrain1,ytest1 = train_test_split(xsm,ysm,test_size = sample_ratio1 , random_state = 42)    
    xtrain2,xtest2,ytrain2,ytest2 = train_test_split(x,y,test_size = sample_ratio2 , random_state = 42)
    
    pipe_lr1 = Pipeline([('scl', StandardScaler()),('pca', PCA()), ('clf', LogisticRegression())]) 
    pipe_lr1.fit(xtrain1, ytrain1)
    print ('\n\n\nDetails of samples with', sample_ratio1,'ratio\n')
    print ('size of x train, y train, x test and y test samples is',xtrain1.shape,ytrain1.shape,xtest1.shape,ytest1.shape, 'respectively')
    print('Test Accuracy for above sample is: %.3f' % pipe_lr1.score(xtest1, ytest1))
    
    pipe_lr2 = Pipeline([('scl', StandardScaler()), ('pca', PCA()),('clf1', LogisticRegression())]) 
    pipe_lr2.fit(xtrain2, ytrain2) 
    print ('\n\n\nDetails of samples with', sample_ratio2,'ratio\n')
    print ('size of x train, y train, x test and y test samples is',xtrain2.shape,ytrain2.shape,xtest2.shape,ytest2.shape ,'respectively')
    print('Test Accuracy for above sample is: %.3f' % pipe_lr2.score(xtest2, ytest2))
In [54]:
diff_sample_test (x,y,0.20,0.90)
# We can see even with changing the sample sizes models performance is quite good,
# certainly scaling and dimension reduction enhances the data resulting in better model performances 
shape of X and Y data set before applying enhancement is (1567, 129) (1567,) respectively



Details of samples with 0.2 ratio

size of x train, y train, x test and y test samples is (2340, 129) (2340,) (586, 129) (586,) respectively
Test Accuracy for above sample is: 0.840



Details of samples with 0.9 ratio

size of x train, y train, x test and y test samples is (156, 129) (156,) (1411, 129) (1411,) respectively
Test Accuracy for above sample is: 0.899
In [55]:
# Lets try using all the models and find the best one for our data set
from sklearn.naive_bayes import GaussianNB
from sklearn.tree import DecisionTreeClassifier
from sklearn.neighbors import KNeighborsClassifier
from sklearn.svm import SVC
from sklearn.svm import SVR
from sklearn.ensemble import RandomForestClassifier
from sklearn.ensemble import BaggingClassifier
from sklearn.ensemble import AdaBoostClassifier
from sklearn.ensemble import GradientBoostingClassifier

models = []
models.append(('GaussianNaiveBayes', GaussianNB()))
models.append(('DecisionTreeClassifier', DecisionTreeClassifier()))
models.append(('KNeighborsClassifier', KNeighborsClassifier()))
models.append(('SVC', SVC()))
models.append(('RandomForestClassifier', RandomForestClassifier()))
models.append(('BaggingClassifier', BaggingClassifier()))
models.append(('AdaBoostClassifier', AdaBoostClassifier()))
models.append(('GradientBoostingClassifier', GradientBoostingClassifier()))

Accuracy = []
recall = []
MName = []

for name, model in models:
    #stratified_kfold_CV_all = StratifiedKFold(n_splits = 10, random_state = 1)
    #StatifiedKF_results_all = cross_val_score(model, X_train_sc_res,y_train_sc_res, cv = stratified_kfold_CV)
    name = model.fit(X_train_sc_res,y_train_sc_res)
    #results.append(StatifiedKF_results_all)
    #names.append(name)
    #print("%s: %f (%f)" % (name, StatifiedKF_results_all.mean(), StatifiedKF_results_all.std()))
    # Prediction on of test data
    y_pred = name.predict(X_test_sc)
    score = name.score(X_test_sc, y_test_sc)
    Accuracy.append(score)
    MName.append(str(name))
    recall.append(metrics.recall_score(y_test_sc, y_pred))
    

# Let's measure the accuracy of this model's prediction
    print('\n\nAccuracy of the ', name,'model is', score*100)
#We can see that models performance is increased due to scaled values
    print('\nClassification Report:')
    print(metrics.classification_report(y_test_sc, y_pred))
    print('\n Confusion Matrix:')
    cm = plot_confusion_matrix(name,X_test_sc,y_test_sc)
    print (cm)
    plt.show()
    

Accuracy of the  GaussianNB() model is 53.71549893842887

Classification Report:
              precision    recall  f1-score   support

          -1       0.94      0.54      0.68       439
           1       0.07      0.50      0.13        32

    accuracy                           0.54       471
   macro avg       0.51      0.52      0.41       471
weighted avg       0.88      0.54      0.65       471


 Confusion Matrix:
<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay object at 0x000001ECD99952E0>

Accuracy of the  DecisionTreeClassifier() model is 77.07006369426752

Classification Report:
              precision    recall  f1-score   support

          -1       0.94      0.81      0.87       439
           1       0.09      0.25      0.13        32

    accuracy                           0.77       471
   macro avg       0.51      0.53      0.50       471
weighted avg       0.88      0.77      0.82       471


 Confusion Matrix:
<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay object at 0x000001ECD98D1E50>

Accuracy of the  KNeighborsClassifier() model is 45.22292993630573

Classification Report:
              precision    recall  f1-score   support

          -1       0.96      0.43      0.59       439
           1       0.09      0.78      0.16        32

    accuracy                           0.45       471
   macro avg       0.53      0.60      0.38       471
weighted avg       0.90      0.45      0.56       471


 Confusion Matrix:
<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay object at 0x000001ECD99952E0>

Accuracy of the  SVC() model is 93.41825902335457

Classification Report:
              precision    recall  f1-score   support

          -1       0.94      1.00      0.97       439
           1       0.60      0.09      0.16        32

    accuracy                           0.93       471
   macro avg       0.77      0.54      0.56       471
weighted avg       0.91      0.93      0.91       471


 Confusion Matrix:
<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay object at 0x000001ECD9F59640>

Accuracy of the  RandomForestClassifier() model is 92.1443736730361

Classification Report:
              precision    recall  f1-score   support

          -1       0.93      0.99      0.96       439
           1       0.14      0.03      0.05        32

    accuracy                           0.92       471
   macro avg       0.54      0.51      0.51       471
weighted avg       0.88      0.92      0.90       471


 Confusion Matrix:
<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay object at 0x000001ECD9F5E040>

Accuracy of the  BaggingClassifier() model is 87.04883227176221

Classification Report:
              precision    recall  f1-score   support

          -1       0.93      0.93      0.93       439
           1       0.06      0.06      0.06        32

    accuracy                           0.87       471
   macro avg       0.50      0.50      0.50       471
weighted avg       0.87      0.87      0.87       471


 Confusion Matrix:
<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay object at 0x000001ECDA2D7550>

Accuracy of the  AdaBoostClassifier() model is 80.67940552016985

Classification Report:
              precision    recall  f1-score   support

          -1       0.94      0.84      0.89       439
           1       0.13      0.31      0.18        32

    accuracy                           0.81       471
   macro avg       0.54      0.58      0.54       471
weighted avg       0.89      0.81      0.84       471


 Confusion Matrix:
<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay object at 0x000001ECD9F59F10>

Accuracy of the  GradientBoostingClassifier() model is 86.62420382165605

Classification Report:
              precision    recall  f1-score   support

          -1       0.94      0.92      0.93       439
           1       0.12      0.16      0.14        32

    accuracy                           0.87       471
   macro avg       0.53      0.54      0.53       471
weighted avg       0.88      0.87      0.87       471


 Confusion Matrix:
<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay object at 0x000001ECDA2D7430>
In [56]:
df = pd.DataFrame()
df['Model_Name'] = MName
df['Accuracy'] = Accuracy
df['Recall'] = recall
print (df)
plt.plot(Accuracy,'g*', label = 'Accuracy')
plt.plot(recall,'ro', label = 'Recall')
plt.legend()
plt.show()
                     Model_Name  Accuracy   Recall
0                  GaussianNB()  0.537155  0.50000
1      DecisionTreeClassifier()  0.770701  0.25000
2        KNeighborsClassifier()  0.452229  0.78125
3                         SVC()  0.934183  0.09375
4      RandomForestClassifier()  0.921444  0.03125
5           BaggingClassifier()  0.870488  0.06250
6          AdaBoostClassifier()  0.806794  0.31250
7  GradientBoostingClassifier()  0.866242  0.15625

We can see that SVC, RandomForestClassifier, BaggingClassifier,AdaBoostClassifier and GradientBoostingClassifier performs better with Accuracy more than 80%, however when it comes in inferencing how much conductors will fail KNN model is out performing all other models.

Hence with agreement with SME, If the agreement is for having highest accuracy in predicting correct conductors we can choose SVC model and if the agreement is for having a model which will prioritize identitfying fail conductors against identifying pass conductors, we will choose KNN model

So lets search for the best hyper parameter for above two models and see if the performance is enhanced or not

In [57]:
# Lets define hyper parameter 
# specify parameters and distributions to sample from
SVC_param = {"kernel" : ['linear', 'poly', 'rbf', 'sigmoid'],
              "gamma" : ['scale', 'auto']}

# run Grid search
grid_search = GridSearchCV(SVC(), param_grid=SVC_param)
grid_search.fit(X_train_sc_res,y_train_sc_res)
print('Parameters suggested for SVC as per Grid search CV', grid_search.best_params_)
print('Accuracy for best SVC as per Grid search CV', grid_search.best_score_)
Parameters suggested for SVC as per Grid search CV {'gamma': 'auto', 'kernel': 'rbf'}
Accuracy for best SVC as per Grid search CV 0.9921855805355119
In [58]:
KNN_param = {'n_neighbors': list(range(1,9)),
             'algorithm': ('auto', 'ball_tree', 'kd_tree' , 'brute') }

# run Grid search
knn_grid_search = GridSearchCV(KNeighborsClassifier(), param_grid=KNN_param)
knn_grid_search.fit(X_train_sc_res,y_train_sc_res)
print('Parameters suggested for Random Forest as per Grid search CV', knn_grid_search.best_params_)
print('Accuracy for best Random Forest as per Grid search CV', knn_grid_search.best_score_)
Parameters suggested for Random Forest as per Grid search CV {'algorithm': 'auto', 'n_neighbors': 2}
Accuracy for best Random Forest as per Grid search CV 0.8193464130240324

So we have best hyper parameters for both SVC and KNN models
Lets create both models individually and check the classificaiton report respectively for the future data set

In [59]:
supersvc = SVC(gamma= 'auto', kernel= 'rbf')
supersvc.fit(X_train_sc_res,y_train_sc_res)

# Prediction on of test data
y_pred = supersvc.predict(X_test_sc)
supersvc_score = supersvc.score(X_test_sc, y_test_sc)

# Let's measure the accuracy of this model's prediction
print('Accuracy of the SVC model is', supersvc_score*100)
#We can see that models performance is increased due to scaled values
print('\n\n Classification Report:')
print(metrics.classification_report(y_test_sc, y_pred))
print('\n\n Confusion Matrix:')
print(plot_confusion_matrix(supersvc,X_test_sc,y_test_sc))
Accuracy of the SVC model is 93.20594479830149


 Classification Report:
              precision    recall  f1-score   support

          -1       0.93      1.00      0.96       439
           1       0.50      0.03      0.06        32

    accuracy                           0.93       471
   macro avg       0.72      0.51      0.51       471
weighted avg       0.90      0.93      0.90       471



 Confusion Matrix:
<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay object at 0x000001ECDAB8E3A0>
In [60]:
super_KNN = KNeighborsClassifier(algorithm= 'auto', n_neighbors =2)
super_KNN.fit(X_train_sc_res,y_train_sc_res)

# Prediction on of test data
y_pred = super_KNN.predict(X_test_sc)
super_KNN_score = super_KNN.score(X_test_sc, y_test_sc)

# Let's measure the accuracy of this model's prediction
print('Accuracy of the KNN model is', super_KNN_score*100)
#We can see that models performance is increased due to scaled values
print('\n\n Classification Report:')
print(metrics.classification_report(y_test_sc, y_pred))
print('\n\n Confusion Matrix:')
print(plot_confusion_matrix(super_KNN,X_test_sc,y_test_sc))
Accuracy of the KNN model is 66.45435244161358


 Classification Report:
              precision    recall  f1-score   support

          -1       0.94      0.69      0.79       439
           1       0.08      0.38      0.13        32

    accuracy                           0.66       471
   macro avg       0.51      0.53      0.46       471
weighted avg       0.88      0.66      0.75       471



 Confusion Matrix:
<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay object at 0x000001ECD64CE490>

We can see that performance of SVC even after searching the best hyper parameters is maintained to 93%. However, performance for KNN model with hyper tuning is reduced w.r.t its prime motive of predicting fail conductors, hence we can choose not to hypertune KNN model and use it in automode completely.

Importing Future data set and predicting target variable for this data set

In [75]:
future_data = pd.read_excel('Future_predictions.xlsx')
In [76]:
future_data.shape
Out[76]:
(18, 591)
In [77]:
future_data.isnull().sum().sum()
Out[77]:
520
In [78]:
future_x = future_data.drop(labels = 'Time', axis = 1)
In [79]:
# Reducing to top 75 supporting features

RFmodel = RandomForestClassifier(bootstrap= True, criterion= 'gini', max_depth= None)
RFmodel.fit(x,y)
RFmodel.feature_importances_
Out[79]:
array([0.01250188, 0.00454851, 0.01183385, 0.00427229, 0.00749766,
       0.00578184, 0.00845835, 0.00474512, 0.01213856, 0.00758788,
       0.00650453, 0.00616132, 0.00598408, 0.01353885, 0.00610327,
       0.00707871, 0.00343864, 0.00950082, 0.01052765, 0.00760384,
       0.02825403, 0.00658387, 0.00812971, 0.01224884, 0.02043785,
       0.01813056, 0.0055625 , 0.0125629 , 0.00728728, 0.01048659,
       0.00788983, 0.00682033, 0.0106956 , 0.00562919, 0.00750529,
       0.00726998, 0.0049119 , 0.00681966, 0.00515747, 0.00533573,
       0.00882911, 0.00745891, 0.00389374, 0.00842129, 0.00625526,
       0.00405232, 0.01011734, 0.00671884, 0.00498824, 0.00489368,
       0.00731516, 0.0040101 , 0.00473903, 0.00693572, 0.00580328,
       0.00771801, 0.00839137, 0.0105377 , 0.00905314, 0.0065213 ,
       0.00662652, 0.00977543, 0.01106865, 0.00597724, 0.00789563,
       0.00913616, 0.00619166, 0.00755363, 0.00768448, 0.00591651,
       0.00536885, 0.00777953, 0.00517977, 0.00354475, 0.01054586,
       0.00608641, 0.01500123, 0.01002834, 0.00866269, 0.00584775,
       0.00888806, 0.00946957, 0.00494864, 0.00679646, 0.00818519,
       0.01087528, 0.00781509, 0.00617515, 0.00508439, 0.00600275,
       0.00808108, 0.00472966, 0.01048855, 0.        , 0.00769813,
       0.00572246, 0.00598348, 0.0035884 , 0.00589246, 0.00620396,
       0.00679405, 0.00741007, 0.00446738, 0.00910528, 0.01139281,
       0.00666362, 0.00366073, 0.00645957, 0.0137689 , 0.0043151 ,
       0.00652834, 0.00870401, 0.00139057, 0.00910181, 0.0057988 ,
       0.00463887, 0.00507055, 0.00796042, 0.00841738, 0.0102278 ,
       0.01564326, 0.00972442, 0.00564035, 0.00884027, 0.01169355,
       0.01080784, 0.00440848, 0.00775433, 0.00493128])
In [80]:
imp_features = np.argsort(RFmodel.feature_importances_)[0:84]
future_x_reduced = future_x[imp_features]
future_x_reduced.head()
Out[80]:
93 112 16 73 97 106 42 51 45 3 109 126 102 1 115 91 52 7 49 36 128 82 48 116 88 38 72 39 70 26 33 122 95 5 114 54 79 98 69 63 96 12 89 75 14 11 87 66 99 44 107 10 59 110 21 60 105 47 100 83 37 31 53 15 35 28 50 101 41 4 34 67 9 19 68 94 55 127 71 86 30 64 117 90
0 -0.0001 NaN 10.0433 NaN 0 0.0000 70 218.3174 130.3691 1411.1265 NaN 3.353 0.1350 2564.00 748.6115 -0.3274 0 0.1242 1 49.3830 3.188 -0.0044 141.2282 0.9908 1747.6049 86.9555 NaN 117.5132 608.1700 1.7730 9.5126 2.639 0.0003 100 0 4.841 -0.0083 0.3974 1 16.1445 -0.2786 202.4396 0.1841 0.0126 7.9558 0.9455 0.9690 693.7724 -0.0251 10.1841 -0.2468 -0.0034 -1.7264 NaN -5419.00 350.9264 0.0056 1.3072 0.0002 7.2163 66.3141 3.5191 4.592 414.8710 64.2588 64.2333 624.3145 0.0002 4.515 1.3602 50.6170 0.9226 0.0162 12.5190 148.6009 0.0001 2834 0.4098 84.0793 2.3895 0.1632 21.7264 58.4306 8671.9301
1 0.0000 NaN 9.2599 NaN 0 0.0000 70 205.1695 133.1727 1463.6606 NaN 2.771 -0.0752 2465.14 731.2517 0.1455 0 0.1247 1 49.3404 3.272 0.0017 145.8445 0.9902 1931.6464 87.5241 NaN 118.1188 620.3582 2.0143 9.7997 2.541 0.0001 100 0 4.842 -0.0358 -0.9353 1 10.9036 0.5854 200.5470 0.1874 -0.0039 10.1548 0.9627 0.9894 697.1964 -0.0158 10.0373 0.0772 -0.0148 0.8073 NaN -5441.50 352.0073 0.0015 1.2887 -0.0004 6.8043 64.9193 3.4171 4.590 414.7347 64.2828 68.4222 631.2618 -0.0004 2.773 0.8294 50.6596 1.1598 -0.0005 12.4608 154.3709 -0.0005 2853 0.4138 82.3494 2.3754 0.2102 19.1927 58.6680 8407.0299
2 -0.0013 0.4684 9.3144 485.2665 0 0.0013 70 185.7574 131.8027 1698.0172 NaN 3.094 0.0134 2559.94 718.5777 0.0553 0 0.1241 1 49.8470 3.272 0.0287 141.0845 0.9899 1685.8514 84.7327 140.6972 118.6128 625.9636 2.0295 8.6590 2.882 0.0002 100 0 4.748 -0.0054 -0.1427 1 11.3019 -0.1343 202.0179 0.1497 -0.0078 9.5157 0.9615 0.9880 710.5095 0.1218 9.8783 -0.0301 0.0013 23.8245 NaN -5447.75 364.5364 -0.0006 1.2992 0.0006 7.1041 65.8389 3.5986 4.486 416.7075 64.1114 67.1333 637.2655 -0.0001 5.434 1.5102 50.1530 0.8694 0.0041 12.5404 145.8000 0.0000 2936 0.4777 84.7681 2.4532 0.1734 16.1755 58.4808 9317.1698
3 -0.0021 0.4647 9.6924 464.9735 0 0.0021 70 189.9079 131.8027 909.7926 NaN 2.480 -0.0699 2479.90 709.0867 0.0697 0 0.1217 1 49.4900 3.119 0.0277 142.5427 0.9906 1752.0968 86.6867 160.3210 117.0442 625.2945 2.0038 8.6789 3.132 0.0002 100 0 4.748 0.0676 0.0177 1 13.5597 0.0411 201.8482 0.1958 -0.0555 9.6052 0.9629 0.9904 710.4043 -0.0195 9.9305 -0.0483 -0.0033 24.3791 NaN -5468.25 361.4582 0.0003 1.3027 -0.0002 7.5925 65.1951 3.3813 4.486 422.2894 64.1125 62.9333 637.3727 0.0000 1.279 1.3204 50.5100 0.9761 -0.0124 12.4782 147.6545 -0.0001 2936 0.5176 70.2289 2.4004 0.2071 15.6209 58.6635 8205.7000
4 -0.0001 NaN 10.3387 NaN 0 0.0000 70 233.5491 176.3136 1326.5200 NaN 3.027 0.0696 2502.87 796.5950 0.0448 0 0.1235 1 49.7520 3.299 -0.0048 138.0882 0.9908 1828.3846 86.1468 NaN 121.4364 645.7636 1.9912 8.7677 3.148 -0.0001 100 0 4.894 0.0034 -0.6704 1 21.9782 0.2189 201.9424 0.1829 -0.0534 10.5661 0.9569 0.9902 745.6025 -0.0167 10.4091 -0.0799 -0.0072 -12.2945 NaN -5476.25 355.0809 0.0078 1.0341 0.0004 7.5017 66.1542 3.2728 4.624 420.5925 64.1511 62.8333 667.7418 -0.0003 2.209 1.5334 50.2480 0.9256 -0.0031 12.4735 146.6636 -0.0001 2865 0.5328 65.8417 2.4530 0.2696 32.2945 58.3858 9014.4600
In [81]:
future_x_reduced.describe().T
Out[81]:
count mean std min 25% 50% 75% max
93 18.0 -0.000883 0.001360 -0.0033 -0.001800 -0.00085 -0.000100 0.0018
112 11.0 0.464391 0.004575 0.4564 0.461150 0.46470 0.466750 0.4727
16 18.0 9.738322 0.387699 9.1999 9.436200 9.69850 10.032225 10.4109
73 8.0 469.437937 6.680888 464.2860 465.804650 468.06705 469.301075 485.2665
97 18.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
106 18.0 0.000933 0.001272 -0.0019 0.000000 0.00085 0.001775 0.0033
42 18.0 70.000000 0.000000 70.0000 70.000000 70.00000 70.000000 70.0000
51 18.0 190.206028 45.206035 112.7524 152.852575 198.06390 217.976500 255.6310
45 18.0 139.672172 11.478393 120.2818 132.552300 139.79000 142.599300 176.3136
3 18.0 1200.046806 255.818978 877.6266 1004.469200 1152.30130 1389.974875 1698.0172
109 0.0 NaN NaN NaN NaN NaN NaN NaN
126 18.0 2.800000 0.214799 2.4800 2.645000 2.77050 2.854000 3.3530
102 18.0 0.020028 0.061977 -0.0752 -0.010250 0.00910 0.049775 0.1638
1 18.0 2526.248889 70.409195 2428.3700 2479.525000 2523.53000 2560.637500 2690.1500
115 18.0 742.226317 42.219709 636.9547 726.798325 748.32585 767.609250 806.2734
91 18.0 -0.027594 0.115585 -0.3274 -0.091900 -0.00500 0.044100 0.1455
52 18.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
7 18.0 0.122056 0.002388 0.1185 0.119950 0.12230 0.124075 0.1257
49 18.0 1.000000 0.000000 1.0000 1.000000 1.00000 1.000000 1.0000
36 18.0 49.628617 0.186347 49.3404 49.495175 49.55155 49.810100 49.9405
128 18.0 3.280167 0.101508 3.1190 3.207000 3.27200 3.362000 3.4420
82 18.0 0.011356 0.031623 -0.1003 0.001025 0.02405 0.028775 0.0356
48 18.0 139.389994 3.023645 136.0836 137.266150 138.15270 140.843150 146.4855
116 18.0 0.988294 0.006531 0.9692 0.990200 0.99055 0.990775 0.9911
88 18.0 1773.365767 75.059770 1632.3120 1720.881125 1764.71245 1827.816225 1931.6464
38 18.0 86.740378 0.946658 84.7327 86.447825 86.74930 87.009350 88.3312
72 8.0 157.012075 9.026895 140.6972 151.653225 158.88595 161.117125 170.5815
39 18.0 118.255900 1.757665 116.5360 117.137900 117.63820 118.523750 122.0886
70 18.0 627.287767 10.565195 608.1700 619.602050 626.75225 635.602050 645.7636
26 18.0 1.667467 0.468792 0.4390 1.770000 1.78010 2.000650 2.0295
33 18.0 9.064589 0.420413 8.5762 8.691400 8.96300 9.434625 9.7997
122 18.0 2.806500 0.362844 2.2700 2.549500 2.77150 3.144000 3.2630
95 18.0 0.000128 0.000102 -0.0001 0.000100 0.00015 0.000200 0.0003
5 18.0 100.000000 0.000000 100.0000 100.000000 100.00000 100.000000 100.0000
114 18.0 0.000000 0.000000 0.0000 0.000000 0.00000 0.000000 0.0000
54 18.0 4.854056 0.068076 4.7480 4.814250 4.86800 4.915000 4.9310
79 18.0 0.005017 0.031852 -0.0423 -0.007575 0.00000 0.008650 0.0676
98 18.0 -0.111244 0.406094 -0.9353 -0.216500 -0.10710 0.097575 0.6241
69 18.0 1.000000 0.000000 1.0000 1.000000 1.00000 1.000000 1.0000
63 18.0 11.059100 4.154847 5.5936 8.108725 10.56545 12.715000 21.9782
96 18.0 0.036689 0.202023 -0.3062 -0.044325 0.02935 0.139050 0.5854
12 18.0 201.648722 6.842171 192.9787 200.490750 201.98015 202.344475 226.0086
89 18.0 0.325056 0.402583 0.1497 0.172900 0.19045 0.203150 1.4727
75 18.0 -0.010433 0.020641 -0.0555 -0.017800 -0.00970 0.001650 0.0227
14 18.0 10.437922 1.684240 7.9558 9.210225 9.88440 12.099525 13.6872
11 18.0 0.955267 0.008500 0.9433 0.946150 0.95865 0.961575 0.9699
87 18.0 0.981283 0.010189 0.9642 0.969125 0.98815 0.989300 0.9906
66 18.0 714.938828 14.263917 693.7724 704.799750 712.57435 727.037275 745.6025
99 18.0 0.008739 0.045102 -0.0419 -0.018800 -0.00510 0.020450 0.1218
44 18.0 9.959256 0.202864 9.7235 9.793700 9.91795 10.055825 10.4091
107 18.0 -0.038622 0.112880 -0.2601 -0.072000 -0.02260 0.027925 0.1359
10 18.0 -0.001594 0.008882 -0.0154 -0.005875 -0.00290 0.001300 0.0216
59 18.0 13.809850 14.968587 -12.2945 -0.692700 21.52180 26.505225 29.1309
110 0.0 NaN NaN NaN NaN NaN NaN NaN
21 18.0 -5018.138889 1354.173579 -6154.0000 -5721.062500 -5458.00000 -5367.000000 -1431.5000
60 18.0 358.418494 5.352772 350.9264 352.345875 360.18955 362.942075 365.0464
105 18.0 0.000867 0.003325 -0.0052 -0.000750 0.00025 0.002650 0.0078
47 18.0 1.141200 0.153443 0.8974 0.976875 1.19310 1.260575 1.3072
100 18.0 0.000061 0.000366 -0.0004 -0.000200 0.00005 0.000300 0.0008
83 18.0 7.308333 0.562315 6.2166 6.879250 7.49290 7.582850 8.4126
37 18.0 65.855422 0.587223 64.9193 65.195100 66.10835 66.327675 66.5050
31 18.0 3.489156 0.084033 3.2728 3.459175 3.50480 3.521450 3.6651
53 18.0 4.590944 0.056058 4.4860 4.563750 4.60800 4.636000 4.6470
15 18.0 417.363083 5.290284 408.4017 414.365625 416.29635 420.562525 428.9826
35 18.0 64.149456 0.151875 63.8294 64.096625 64.13180 64.240675 64.4021
28 18.0 64.335794 2.741885 60.2444 62.575000 63.36670 67.108300 68.7111
50 18.0 637.241556 10.886987 621.4300 630.275450 637.50815 640.137250 667.7418
101 18.0 -0.000050 0.000195 -0.0004 -0.000100 -0.00005 0.000075 0.0003
41 18.0 3.227389 1.281761 1.2790 2.324500 3.12050 3.951500 5.4340
4 18.0 1.208883 0.284415 0.7884 0.871025 1.32040 1.395000 1.5334
34 18.0 50.371394 0.186354 50.0595 50.189900 50.44850 50.504825 50.6596
67 18.0 0.959961 0.078151 0.8692 0.911575 0.93570 0.992575 1.1598
9 18.0 0.003572 0.017393 -0.0270 -0.010075 0.01275 0.016125 0.0250
19 18.0 12.388433 0.421946 10.7029 12.461150 12.47610 12.524475 12.5404
68 18.0 147.609500 3.522391 142.5155 144.621175 146.90225 150.183900 154.3709
94 18.0 -0.000067 0.000146 -0.0005 -0.000100 -0.00005 0.000000 0.0002
55 18.0 2875.166667 31.267818 2834.0000 2856.000000 2865.00000 2884.000000 2936.0000
127 18.0 0.451594 0.073217 0.3273 0.413800 0.46220 0.515800 0.5328
71 18.0 82.903950 17.276064 57.0841 70.264350 81.24785 90.316525 112.0904
86 18.0 2.402406 0.050233 2.2944 2.367525 2.40005 2.453150 2.4704
30 18.0 0.196739 0.030673 0.1394 0.176150 0.19840 0.209675 0.2696
64 18.0 18.412372 6.017118 10.8691 13.494775 17.63320 21.592975 32.2945
117 18.0 58.569439 0.720623 56.5635 58.443150 58.65975 58.811875 59.5776
90 18.0 8714.982761 428.395594 7869.7000 8502.547475 8730.71510 9079.080000 9317.1698
In [82]:
# We can see that many columns have too many null values, so columns which have null values more than 70% can be droppped
# as majority of the data is missing imputing and creating majority of the artificial data is of no use in above case
# SO columns having null values more than roughly 1000 can be dropped
counter  = 0

for columns in future_x_reduced.columns:
    if future_x_reduced[columns].isnull().sum() >= 15:
        counter = counter + 1
        print( columns , 'Column has', future_x_reduced[columns].isnull().sum() , ' null values, hence can be dropped')
        del future_x_reduced[columns]
        

print('New shape of the data set after deleting above', counter ,' columns is', future_x_reduced.shape)
109 Column has 18  null values, hence can be dropped
110 Column has 18  null values, hence can be dropped
New shape of the data set after deleting above 2  columns is (18, 82)
In [83]:
counter  = 0
for columns in future_x_reduced.columns:
    if future_x_reduced[columns].min() == future_x_reduced[columns].median() and future_x_reduced[columns].max() == future_x_reduced[columns].median():
        counter = counter + 1
        print( columns , 'Column has single value ', future_x_reduced[columns].median(), ', hence can be dropped')
        del future_x_reduced[columns]
        

print('New shape of the data set after deleting above', counter ,' columns is', future_x_reduced.shape)
97 Column has single value  0.0 , hence can be dropped
42 Column has single value  70.0 , hence can be dropped
52 Column has single value  0.0 , hence can be dropped
49 Column has single value  1.0 , hence can be dropped
5 Column has single value  100.0 , hence can be dropped
114 Column has single value  0.0 , hence can be dropped
69 Column has single value  1.0 , hence can be dropped
New shape of the data set after deleting above 7  columns is (18, 75)
In [84]:
future_x_reduced.isnull().sum().sum()
Out[84]:
27
In [85]:
# Since we do not really know much about each particular feature, we will fill the null values with the mean value 

#Replace blank valus with Nan values
future_x_reduced = future_x_reduced.replace('', np.nan)

#Replace the Null value with the mean value of each column
for columns in future_x_reduced.columns:
    mean = future_x_reduced[columns].mean()
    future_x_reduced[columns] = future_x_reduced[columns].fillna(mean)
In [86]:
future_x_reduced.isnull().sum().sum()
Out[86]:
0
In [87]:
final_svc = SVC(gamma= 'auto', kernel= 'rbf')
final_svc.fit(X_train_sc_res,y_train_sc_res)
Future_PassFail_svc = final_svc.predict(future_x_reduced)
print ('Prediction on FUture data set with SVC model is\n',Future_PassFail_svc)
Prediction on FUture data set with SVC model is
 [-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1]
In [88]:
final_KNN = KNeighborsClassifier()
final_KNN.fit(X_train_sc_res,y_train_sc_res)
Future_PassFail_knn = final_KNN.predict(future_x_reduced)
print('Prediction on Future data set with Random Forest model is\n',Future_PassFail_knn)
Prediction on Future data set with Random Forest model is
 [-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1]

Conclusion and improvisation:

  1. FirstlyBy using techiniques like Scaling and reducing dimensions based on the importance can enhance models performance
  2. We can drop or clean data set using many techiniques like, low - variance columns, columns with high number of null values, columns with same valur in all rows PCA and Random forest
  3. Different CV techniques can give us the ratio of the models performance based on which we can infer the range of model's performance in production
  4. Grid search can give us best parameter of the model for enhancing its accuracy, however it can not always be help full as we saw in our data set, if the objective is to identify faulty condutors then we should use KNN on automode instead of best parameters.
  5. As a part of improvisations high efforts should be made while collecting the data, Quality of the data is the topmost factor of data science, in our case we had too many null values, vague columns, 90% of the data have presence of outliers and most of all, target column is completely imbalance. Such data requires huge data manipulations which eventually tempers the original data. Hence probability of Model not performing well in production increases.
In [ ]: